WorldWideScience

Sample records for field theory analysis

  1. Dimensional analysis in field theory

    International Nuclear Information System (INIS)

    Stevenson, P.M.

    1981-01-01

    Dimensional Transmutation (the breakdown of scale invariance in field theories) is reconciled with the commonsense notions of Dimensional Analysis. This makes possible a discussion of the meaning of the Renormalisation Group equations, completely divorced from the technicalities of renormalisation. As illustrations, I describe some very farmiliar QCD results in these terms

  2. Astrophysical data analysis with information field theory

    International Nuclear Information System (INIS)

    Enßlin, Torsten

    2014-01-01

    Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented

  3. Astrophysical data analysis with information field theory

    Science.gov (United States)

    Enßlin, Torsten

    2014-12-01

    Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

  4. Astrophysical data analysis with information field theory

    Energy Technology Data Exchange (ETDEWEB)

    Enßlin, Torsten, E-mail: ensslin@mpa-garching.mpg.de [Max Planck Institut für Astrophysik, Karl-Schwarzschild-Straße 1, D-85748 Garching, Germany and Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, D-80539 München (Germany)

    2014-12-05

    Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

  5. Geophysical Field Theory

    International Nuclear Information System (INIS)

    Eloranta, E.

    2003-11-01

    The geophysical field theory includes the basic principles of electromagnetism, continuum mechanics, and potential theory upon which the computational modelling of geophysical phenomena is based on. Vector analysis is the main mathematical tool in the field analyses. Electrostatics, stationary electric current, magnetostatics, and electrodynamics form a central part of electromagnetism in geophysical field theory. Potential theory concerns especially gravity, but also electrostatics and magnetostatics. Solid state mechanics and fluid mechanics are central parts in continuum mechanics. Also the theories of elastic waves and rock mechanics belong to geophysical solid state mechanics. The theories of geohydrology and mass transport form one central field theory in geophysical fluid mechanics. Also heat transfer is included in continuum mechanics. (orig.)

  6. String theory or field theory?

    International Nuclear Information System (INIS)

    Marshakov, Andrei V

    2002-01-01

    The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of string theory in the modern picture of the physical world. Even though quantum field theory describes a wide range of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments which are our concern in this review. (reviews of topical problems)

  7. String theory or field theory?

    International Nuclear Information System (INIS)

    Marshakov, A.V.

    2002-01-01

    The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments, which are our concern in this review [ru

  8. Analysis of interacting quantum field theory in curved spacetime

    International Nuclear Information System (INIS)

    Birrell, N.D.; Taylor, J.G.

    1980-01-01

    A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given. Reduction formulas for S-matrix elements in terms of vacuum Green's functions are derived, special attention being paid to the possibility that the ''in'' and ''out'' vacuum states may not be equivalent. Green's functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for lambdaphi 3 /sub() 4,6/ field theories. The extension of these techniques to curved spacetimes is considered. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, phi 3 /sub( 4 ) is proven renormalizable in a large class of spacetimes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes

  9. Lattice field theories: non-perturbative methods of analysis

    International Nuclear Information System (INIS)

    Weinstein, M.

    1978-01-01

    A lecture is given on the possible extraction of interesting physical information from quantum field theories by studying their semiclassical versions. From the beginning the problem of solving for the spectrum states of any given continuum quantum field theory is considered as a giant Schroedinger problem, and then some nonperturbative methods for diagonalizing the Hamiltonian of the theory are explained without recourse to semiclassical approximations. The notion of a lattice appears as an artifice to handle the problems associated with the familiar infrared and ultraviolet divergences of continuum quantum field theory and in fact for all but gauge theories. 18 references

  10. Theory of interacting quantum fields

    International Nuclear Information System (INIS)

    Rebenko, Alexei L.

    2012-01-01

    This monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20 th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism.

  11. L_∞ algebras and field theory

    International Nuclear Information System (INIS)

    Hohm, Olaf; Zwiebach, Barton

    2017-01-01

    We review and develop the general properties of L_∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L_∞ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L_∞ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L_∞ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L_∞ algebra for the interacting theory. The analysis suggests that L_∞ algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  12. Braided quantum field theories and their symmetries

    International Nuclear Information System (INIS)

    Sasai, Yuya; Sasakura, Naoki

    2007-01-01

    Braided quantum field theories, proposed by Oeckl, can provide a framework for quantum field theories that possess Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We study Hopf algebra symmetries and such relations in the context of braided quantum field theories. We give the four algebraic conditions among Hopf algebra symmetries and braided quantum field theories that are required for the relations to hold. As concrete examples, we apply our analysis to the Poincare symmetries of two examples of noncommutative field theories. One is the effective quantum field theory of three-dimensional quantum gravity coupled to spinless particles formulated by Freidel and Livine, and the other is noncommutative field theory on the Moyal plane. We also comment on quantum field theory in κ-Minkowski spacetime. (author)

  13. Mass corrections in string theory and lattice field theory

    International Nuclear Information System (INIS)

    Del Debbio, Luigi; Kerrane, Eoin; Russo, Rodolfo

    2009-01-01

    Kaluza-Klein (KK) compactifications of higher-dimensional Yang-Mills theories contain a number of 4-dimensional scalars corresponding to the internal components of the gauge field. While at tree level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1 loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius R is much bigger than the scale of the UV completion (R>>√(α ' ), a), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in N=2, 4 super Yang-Mills is highly suppressed, even if the lattice regularization breaks all supersymmetries explicitly. This is due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.

  14. An application of random field theory to analysis of electron trapping sites in disordered media

    International Nuclear Information System (INIS)

    Hilczer, M.; Bartczak, W.M.

    1993-01-01

    The potential energy surface in a disordered medium is considered a random field and described using the concepts of the mathematical theory of random fields. The preexisting traps for excess electrons are identified with certain regions of excursion (extreme regions) of the potential field. The theory provides an analytical method of statistical analysis of these regions. Parameters of the cavity-averaged potential field, which are provided by computer simulation of a given medium, serve as input data for the analysis. The statistics of preexisting traps are obtained for liquid methanol as a numerical example of the random field method. 26 refs., 6 figs

  15. Unitary field theories

    International Nuclear Information System (INIS)

    Bergmann, P.G.

    1980-01-01

    A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion

  16. Symmetry analysis for anisotropic field theories

    International Nuclear Information System (INIS)

    Parra, Lorena; Vergara, J. David

    2012-01-01

    The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.

  17. The Nonlinear Field Space Theory

    Energy Technology Data Exchange (ETDEWEB)

    Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)

    2016-08-10

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  18. The Nonlinear Field Space Theory

    International Nuclear Information System (INIS)

    Mielczarek, Jakub; Trześniewski, Tomasz

    2016-01-01

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  19. String field theory

    International Nuclear Information System (INIS)

    Kaku, M.

    1987-01-01

    In this article, the authors summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. They also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group they call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU(N). The geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory

  20. L{sub ∞} algebras and field theory

    Energy Technology Data Exchange (ETDEWEB)

    Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY (United States); Zwiebach, Barton [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)

    2017-03-15

    We review and develop the general properties of L{sub ∞} algebras focusing on the gauge structure of the associated field theories. Motivated by the L{sub ∞} homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L{sub ∞} structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L{sub ∞} algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L{sub ∞} algebra for the interacting theory. The analysis suggests that L{sub ∞} algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  1. Analysis of General Power Counting Rules in Effective Field Theory

    CERN Document Server

    Gavela, B M; Manohar, A V; Merlo, L

    2016-01-01

    We derive the general counting rules for a quantum effective field theory (EFT) in $\\mathsf{d}$ dimensions. The rules are valid for strongly and weakly coupled theories, and predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. The size of cross sections is controlled by the $\\Lambda$ power counting of EFT, not by chiral counting, even for chiral perturbation theory ($\\chi$PT). The relation between $\\Lambda$ and $f$ is generalized to $\\mathsf{d}$ dimensions. We show that the naive dimensional analysis $4\\pi$ counting is related to $\\hbar$ counting. The EFT counting rules are applied to $\\chi$PT, to Standard Model EFT and to the non-trivial case of Higgs EFT, which combines the $\\Lambda$ and chiral counting rules within a single theory.

  2. Operator algebras and conformal field theory

    International Nuclear Information System (INIS)

    Gabbiani, F.; Froehlich, J.

    1993-01-01

    We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III 1 factor. The conformal net determined by the algebras of local observables is proven to satisfy Haag duality. The representation of the Moebius group (and presumably of the entire Virasoro algebra) on the vacuum sector of a conformal field theory is uniquely determined by the Tomita-Takesaki modular operators associated with its vacuum state and its conformal net. We then develop the theory of Mebius covariant representations of a conformal net, using methods of Doplicher, Haag and Roberts. We apply our results to the representation theory of loop groups. Our analysis is motivated by the desire to find a 'background-independent' formulation of conformal field theories. (orig.)

  3. Quantum field theory

    International Nuclear Information System (INIS)

    Ryder, L.H.

    1985-01-01

    This introduction to the ideas and techniques of quantum field theory presents the material as simply as possible and is designed for graduate research students. After a brief survey of particle physics, the quantum theory of scalar and spinor fields and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a bridge survey of ''topological'' objects in field theory and assumes a knowledge of quantum mechanics and special relativity

  4. Classical field theory

    CERN Document Server

    Franklin, Joel

    2017-01-01

    Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...

  5. Field theories with subcanonical fields

    International Nuclear Information System (INIS)

    Bigi, I.I.Y.

    1976-01-01

    The properties of quantum field theories with spinor fields of dimension less than the canonical value of 3/2 are studied. As a starting point for the application of common perturbation theory we look for the linear version of these theories. A gange-interaction is introduced and with the aid of power counting the renormalizability of the theory is shown. It follows that in the case of a spinor-field with negative dimension renormalization can only be attained if the interaction has a further symmetry. By this symmetry the theory is determined in an unequivocal way. The gange-interaction introduced in the theory leads to a spontaneous breakdown of scale invariance whereby masses are produced. At the same time the spinor-field operators can now be separated in two orthogonal sections with opposite norm. It is proposed to use the section with negative (positive) norm to describe hadrons (leptons) respectively. (orig./WL) [de

  6. Factorization algebras in quantum field theory

    CERN Document Server

    Costello, Kevin

    2017-01-01

    Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.

  7. Unified field theory

    International Nuclear Information System (INIS)

    Prasad, R.

    1975-01-01

    Results of researches into Unified Field Theory over the past seven years are presented. The subject is dealt with in chapters entitled: the choice of affine connection, algebraic properties of the vector fields, field laws obtained from the affine connection based on the path integral method, application to quantum theory and cosmology, interpretation of physical theory in terms of geometry. (U.K.)

  8. Analysis of family-wise error rates in statistical parametric mapping using random field theory.

    Science.gov (United States)

    Flandin, Guillaume; Friston, Karl J

    2017-11-01

    This technical report revisits the analysis of family-wise error rates in statistical parametric mapping-using random field theory-reported in (Eklund et al. []: arXiv 1511.01863). Contrary to the understandable spin that these sorts of analyses attract, a review of their results suggests that they endorse the use of parametric assumptions-and random field theory-in the analysis of functional neuroimaging data. We briefly rehearse the advantages parametric analyses offer over nonparametric alternatives and then unpack the implications of (Eklund et al. []: arXiv 1511.01863) for parametric procedures. Hum Brain Mapp, 2017. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

  9. Finite discrete field theory

    International Nuclear Information System (INIS)

    Souza, Manoelito M. de

    1997-01-01

    We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)

  10. Effective field theories

    International Nuclear Information System (INIS)

    Mack, G.; Kalkreuter, T.; Palma, G.; Speh, M.

    1992-05-01

    Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low utraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically, the idea is to integrate out the high frequency components of fields. This requires the choice of a 'blockspin', i.e. the specification af a low frequency field as a function of the fundamental fields. These blockspins will be fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspin in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels A from coarse to fine grid in addition to the averaging kernels C which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The special case of a 'lattice' with a single site (the constraint effective potential) is of particular interest. In a higgs model, the effective action reduces in this case to the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data. (orig.)

  11. Effective quantum field theories

    International Nuclear Information System (INIS)

    Georgi, H.M.

    1993-01-01

    The most appropriate description of particle interactions in the language of quantum field theory depends on the energy at which the interactions are studied; the description is in terms of an ''effective field theory'' that contains explicit reference only to those particles that are actually important at the energy being studied. The various themes of the article are: local quantum field theory, quantum electrodynamics, new physics, dimensional parameters and renormalizability, socio-dynamics of particle theory, spontaneously broken gauge theories, scale dependence, grand unified and effective field theories. 2 figs

  12. Field theory

    CERN Multimedia

    1999-11-08

    In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.

  13. Field theory and strings

    International Nuclear Information System (INIS)

    Bonara, L.; Cotta-Ramusino, P.; Rinaldi, M.

    1987-01-01

    It is well-known that type I and heterotic superstring theories have a zero mass spectrum which correspond to the field content of N=1 supergravity theory coupled to supersymmetric Yang-Mills theory in 10-D. The authors study the field theory ''per se'', in the hope that simple consistency requirements will determine the theory completely once one knows the field content inherited from string theory. The simplest consistency requirements are: N=1 supersymmetry; and absence of chiral anomalies. This is what the authors discuss in this paper here leaving undetermined the question of the range of validity of the resulting field theory. As is known, a model of N=1 supergravity (SUGRA) coupled to supersymmetric Yang-Mills (SYM) theory was known in the form given by Chapline and Manton. The coupling of SUGRA to SYM was determined by the definition of the ''field strength'' 3-form H in this paper

  14. Algebraic conformal field theory

    International Nuclear Information System (INIS)

    Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

    1991-11-01

    Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs

  15. Microcanonical quantum field theory

    International Nuclear Information System (INIS)

    Strominger, A.

    1983-01-01

    Euclidean quantum field theory is equivalent to the equilibrium statistical mechanics of classical fields in 4+1 dimensions at temperature h. It is well known in statistical mechanics that the theory of systems at fixed temperature is embedded within the more general and fundamental theory of systems at fixed energy. We therefore develop, in precise analogy, a fixed action (macrocanonical) formulation of quantum field theory. For the case of ordinary renormalizable field theories, we show (with one exception) that the microcanonical is entirely equivalent to the canonical formulation. That is, for some particular fixed value of the total action, the Green's functions of the microcanonical theory are equal, in the bulk limit, to those of the canonical theory. The microcanonical perturbation expansion is developed in some detail for lambdaphi 4 . The particular value of the action for which the two formulations are equivalent can be calculated to all orders in perturbation theory. We prove, using Lehmann's Theorem, that this value is one-half Planck unit per degree of freedom, if fermionic degrees of freedom are counted negatively. This is the 4+1 dimensional analog of the equipartition theorem. The one exception to this is supersymmetric theories. A microcanonical formulation exists if and only if supersymmetry is broken. In statistical mechanics and in field theory there are systems for which the canonical description is pathological, but the microcanonical is not. An example of such a field theory is found in one dimension. A semiclassical expansion of the microcanonical theory is well defined, while an expansion of the canonical theory is hoplessly divergent

  16. Metastability in Field Theory and Statistical Mechanics

    International Nuclear Information System (INIS)

    Carvalho, C.A. de.

    1984-01-01

    After a phase transition analysis which can occur in the framework of a scalar field theory, at finite temperature and in presence of a external field, possibles metastable situations are studied and also how is their relationship with the transitions. In both cases it is used a semiclassical approximation to the theory which, in Statistical Mechanics, corresponds to the droplet-bubble model. (L.C.) [pt

  17. Introduction to gauge field theory

    International Nuclear Information System (INIS)

    Bailin, D.; Love, A.

    1986-01-01

    This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications

  18. Introduction to gauge field theory

    International Nuclear Information System (INIS)

    Bailin, David; Love, Alexander

    1986-01-01

    The book is intended as an introduction to gauge field theory for the postgraduate student of theoretical particle physics. The topics discussed in the book include: path integrals, classical and quantum field theory, scattering amplitudes, feynman rules, renormalisation, gauge field theories, spontaneous symmetry breaking, grand unified theory, and field theories at finite temperature. (UK)

  19. Studies in quantum field theory

    International Nuclear Information System (INIS)

    Bender, C.M.; Mandula, J.E.; Shrauner, J.E.

    1982-01-01

    Washington University is currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large orders; quark condensation in QCD; chiral symmetry breaking; the l/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD

  20. Renormalization of topological field theory

    International Nuclear Information System (INIS)

    Birmingham, D.; Rakowski, M.; Thompson, G.

    1988-11-01

    One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs

  1. Engineering field theory

    CERN Document Server

    Baden Fuller, A J

    2014-01-01

    Engineering Field Theory focuses on the applications of field theory in gravitation, electrostatics, magnetism, electric current flow, conductive heat transfer, fluid flow, and seepage.The manuscript first ponders on electric flux, electrical materials, and flux function. Discussions focus on field intensity at the surface of a conductor, force on a charged surface, atomic properties, doublet and uniform field, flux tube and flux line, line charge and line sink, field of a surface charge, field intensity, flux density, permittivity, and Coulomb's law. The text then takes a look at gravitation

  2. Duality and braiding in twisted quantum field theory

    International Nuclear Information System (INIS)

    Riccardi, Mauro; Szabo, Richard J.

    2008-01-01

    We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality

  3. Perturbative algebraic quantum field theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Lindner, Falk

    2013-08-15

    We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.

  4. Perturbative algebraic quantum field theory at finite temperature

    International Nuclear Information System (INIS)

    Lindner, Falk

    2013-08-01

    We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.

  5. The zero-bin and mode factorization in quantum field theory

    International Nuclear Information System (INIS)

    Manohar, Aneesh V.; Stewart, Iain W.

    2007-01-01

    We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In nonrelativistic field theories, the subtractions remove unphysical pinch singularities in box-type diagrams, and give a derivation of the known pullup mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formulas occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long-standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays

  6. Strings - Links between conformal field theory, gauge theory and gravity

    International Nuclear Information System (INIS)

    Troost, J.

    2009-05-01

    String theory is a candidate framework for unifying the gauge theories of interacting elementary particles with a quantum theory of gravity. The last years we have made considerable progress in understanding non-perturbative aspects of string theory, and in bringing string theory closer to experiment, via the search for the Standard Model within string theory, but also via phenomenological models inspired by the physics of strings. Despite these advances, many deep problems remain, amongst which a non-perturbative definition of string theory, a better understanding of holography, and the cosmological constant problem. My research has concentrated on various theoretical aspects of quantum theories of gravity, including holography, black holes physics and cosmology. In this Habilitation thesis I have laid bare many more links between conformal field theory, gauge theory and gravity. Most contributions were motivated by string theory, like the analysis of supersymmetry preserving states in compactified gauge theories and their relation to affine algebras, time-dependent aspects of the holographic map between quantum gravity in anti-de-Sitter space and conformal field theories in the bulk, the direct quantization of strings on black hole backgrounds, the embedding of the no-boundary proposal for a wave-function of the universe in string theory, a non-rational Verlinde formula and the construction of non-geometric solutions to supergravity

  7. Infrared difficulties with thermal quantum field theories

    International Nuclear Information System (INIS)

    Grandou, T.

    1997-01-01

    Reviewing briefly the two main difficulties encountered in thermal quantum field theories at finite temperature when dealing with the Braaten-Pisarski (BP) resummation program, the motivation is introduced of an analysis relying on the bare perturbation theory, right from the onset. (author)

  8. Quantum field theory

    CERN Document Server

    Mandl, Franz

    2010-01-01

    Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic

  9. Dual double field theory

    Energy Technology Data Exchange (ETDEWEB)

    Bergshoeff, Eric A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook, NY 11794-3636 (United States); Penas, Victor A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Riccioni, Fabio [INFN - Sezione di Roma, Dipartimento di Fisica, Università di Roma “La Sapienza”,Piazzale Aldo Moro 2, 00185 Roma (Italy)

    2016-06-06

    We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for “exotic' dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.

  10. Nonlocal continuum field theories

    CERN Document Server

    2002-01-01

    Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...

  11. Morse theory interpretation of topological quantum field theories

    International Nuclear Information System (INIS)

    Labastida, J.M.F.

    1989-01-01

    Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: Topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained. (orig.)

  12. Axiomatic conformal field theory

    International Nuclear Information System (INIS)

    Gaberdiel, M.R.; Goddard, P.

    2000-01-01

    A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, Moebius invariance rather than full conformal invariance is required but it is shown that every Moebius theory can be extended to a conformal theory by the construction of a Virasoro field. In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained. (orig.)

  13. Band mixing effects in mean field theories

    International Nuclear Information System (INIS)

    Kuyucak, S.; Morrison, I.

    1989-01-01

    The 1/N expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model (IBM). Conversely, comparison with the exact IBM results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the E2 transitions among the ground, β and γ bands are incomplete for the spin dependent terms and it is essential to include band mixing effect for a correct (Mikhailov) analysis of E2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the sd and sdg boson models. 17 refs., 7 figs., 8 tabs

  14. Hamiltonian Anomalies from Extended Field Theories

    Science.gov (United States)

    Monnier, Samuel

    2015-09-01

    We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

  15. Differential algebras in field theory

    International Nuclear Information System (INIS)

    Stora, R.

    1988-01-01

    The applications of differential algebras, as mathematical tools, in field theory are reviewed. The Yang-Mills theories are recalled and the free bosonic string model is treated. Moreover, in the scope of the work, the following topics are discussed: the Faddeev Popov fixed action, in a Feynman like gauge; the structure of local anomalies, including the algebric and the topological theories; the problem of quantizing a degenerate state; and the zero mode problem, in the treatment of the bosonic string conformal gauge. The analysis leads to the conclusion that not much is known about situations where a non involutive distribution is involved

  16. More effective field theory for non-relativistic scattering

    International Nuclear Information System (INIS)

    Kaplan, D.B.

    1997-01-01

    An effective field theory treatment of nucleon-nucleon scattering at low energy shows much promise and could prove to be a useful tool in the study of nuclear matter at both ordinary and extreme densities. The analysis is complicated by the existence a large length scale - the scattering length -which arises due to couplings in the short distance theory being near critical values. I show how this can be dealt with by introducing an explicit s-channel state in the effective field theory. The procedure is worked out analytically in a toy example. I then demonstrate that a simple effective field theory excellently reproduces the 1 S 0 np phase shift up to the pion production threshold. (orig.)

  17. Density-functional theory for internal magnetic fields

    Science.gov (United States)

    Tellgren, Erik I.

    2018-01-01

    A density-functional theory is developed based on the Maxwell-Schrödinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current density-functional theory and an alternative to the paramagnetic current density-functional theory due to Vignale and Rasolt. The energy functional has strong enough convexity properties to allow a formulation that generalizes Lieb's convex analysis formulation of standard density-functional theory. Several variational principles as well as a Hohenberg-Kohn-like mapping between potentials and ground-state densities follow from the underlying convex structure. Moreover, the energy functional can be regarded as the result of a standard approximation technique (Moreau-Yosida regularization) applied to the conventional Schrödinger ground-state energy, which imposes limits on the maximum curvature of the energy (with respect to the magnetic field) and enables construction of a (Fréchet) differentiable universal density functional.

  18. Large N field theories, string theory and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Maldacena, J [Lyman Laboratory of Physics, Harvard University, Cambridge (United States)

    2002-05-15

    We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/ M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions. These lecture notes are based on the Review written by O. Aharony, S. Gubser, J. Maldacena, H. Ooguri and Y. Oz. (author)

  19. Topics in quantum field theory

    International Nuclear Information System (INIS)

    Svaiter, N.F.

    2006-11-01

    This paper presents some important aspects on quantum field theory, covering the following aspects: the triumph and limitations of the quantum field theory; the field theory in curved spaces - Hawking and Unruh-Davies effects; the problem of divergent theory of the zero-point; the problem of the spinning detector and the Trocheries-Takeno vacuum; the field theory at finite temperature - symmetry breaking and phase transition; the problem of the summability of the perturbative series and the perturbative expansion for the strong coupling; quantized fields in presence of classical macroscopic structures; the Parisi-Wu stochastic quantization method

  20. Test-particle motion in Einstein's unified field theory. I. General theory and application to neutral test particles

    International Nuclear Information System (INIS)

    Johnson, C.R.

    1985-01-01

    We develop a method for finding the exact equations of structure and motion of multipole test particles in Einstein's unified field theory: the theory of the nonsymmetric field. The method is also applicable to Einstein's gravitational theory. Particles are represented by singularities in the field. The method is covariant at each step of the analysis. We also apply the method and find both in Einstein's unified field theory and in Einstein's gravitational theory the equations of structure and motion of neutral pole-dipole test particles possessing no electromagnetic multipole moments. In the case of Einstein's gravitational theory the results are the well-known equations of structure and motion of a neutral pole-dipole test particle in a given background gravitational field. In the case of Einstein's unified field theory the results are the same, providing we identify a certain symmetric second-rank tensor field appearing in Einstein's theory with the metric and gravitational field. We therefore discover not only the equations of structure and motion of a neutral test particle in Einstein's unified field theory, but we also discover what field in Einstein's theory plays the role of metric and gravitational field

  1. Topics in two dimensional conformal field theory and three dimensional topological lattice field theory

    International Nuclear Information System (INIS)

    Chung, Stephen-wei.

    1993-01-01

    The authors first construct new parafermions in two-dimensional conformal field theory, generalizing the Z L parafermion theories from integer L to rational L. These non-unitary parafermions have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. String functions of these new parafermion theories are calculated. They also construct new representations of N = 2 superconformal field theories, whose characters are obtained in terms of these new string functions. They then generalize Felder's BRST cohomology method to construct the characters and branching functions of the SU(2) L x SU(2) K /SU(2) K+L coset theories, where one of the (K,L) is an integer. This method of obtaining the branching functions also serves as a check of their new Z L parafermion theories. The next topic is the Lagrangian formulation of conformal field theory. They construct a chiral gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R , which can be different groups. This new construction is beyond the ordinary vector gauged WZW theory, whose gauge group H is a subgroup of both G L and G R . In the special case where H L = H R , the quantum theory of chiral gauged WZW theory is equivalent to that of the vector gauged WZW theory. It can be further shown that the chiral gauged WZW theory is equivalent to [G L /H L ](z) direct-product [G R /H R ](bar z) coset models in conformal field theory. In the second half of this thesis, they construct topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, they impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint

  2. Introduction to string field theory

    International Nuclear Information System (INIS)

    Horowitz, G.T.

    1989-01-01

    A light cone gauge superstring field theory is constructed. The BRST approach is described discussing generalizations to yield gauge invariant free superstring field theory and interacting theory for superstrings. The interaction term is explicitly expressed in terms of first quantized oscillators. A purily cubic action for superstring field theory is also derived. (author)

  3. Further Development of HS Field Theory

    Science.gov (United States)

    Abdurrahman, Abdulmajeed; Faridani, Jacqueline; Gassem, Mahmoud

    2006-04-01

    We present a systematic treatment of the HS Field theory of the open bosonic string and discuss its relationship to other full string field theories of the open bosonic string such as Witten's theory and the CVS theory. In the development of the HS field theory we encounter infinite dimensional matrices arising from the change of representation between the two theories, i.e., the HS field theory and the full string field theory. We give a general procedure of how to invert these gigantic matrices. The inversion of these matrices involves the computation of many infinite sums. We give the values of these sums and state their generalizations arising from considering higher order vertices (i.e., more than three strings) in string field theory. Moreover, we give a general procedure, on how to evaluate the generalized sums, that can be extended to many generic sums of similar properties. We also discuss the conformal operator connecting the HS field theory to that of the CVS string field theory.

  4. Naturality in conformal field theory

    International Nuclear Information System (INIS)

    Moore, G.; Seiberg, N.

    1989-01-01

    We discuss constraints on the operator product coefficients in diagonal and nondiagonal rational conformal field theories. Nondiagonal modular invariants always arise from automorphisms of the fusion rule algebra or from extensions of the chiral algebra. Moreover, when the chiral algebra has been maximally extended a strong form of the naturality principle of field theory can be proven for rational conformal field theory: operator product coefficients vanish if and only if the corresponding fusion rules vanish; that is, if and only if the vanishing can be understood in terms of a symmetry. We illustrate these ideas with several examples. We also generalize our ideas about rational conformal field theories to a larger class of theories: 'quasi-rational conformal field theories' and we explore some of their properties. (orig.)

  5. The utility of quantum field theory

    International Nuclear Information System (INIS)

    Dine, Michael

    2001-01-01

    This talk surveys a broad range of applications of quantum field theory, as well as some recent developments. The stress is on the notion of effective field theories. Topics include implications of neutrino mass and a possible small value of sin(2β), supersymmetric extensions of the standard model, the use of field theory to understand fundamental issues in string theory (the problem of multiple ground states and the question: does string theory predict low energy supersymmetry), and the use of string theory to solve problems in field theory. Also considered are a new type of field theory, and indications from black hole physics and the cosmological constant problem that effective field theories may not completely describe theories of gravity. (author)

  6. A symplectic framework for field theories

    International Nuclear Information System (INIS)

    Kijowski, J.; Tulczyjew, W.M.

    1979-01-01

    These notes are concerned with the formulation of a new conceptual framework for classical field theories. Although the formulation is based on fairly advanced concepts of symplectic geometry these notes cannot be viewed as a reformulation of known structures in more rigorous and elegant torns. Our intention is rather to communicate to theoretical physicists a set of new physical ideas. We have chosen for this purpose the language of local coordinates which is more elementary and more widely known than the abstract language of modern differntial geometry. Our emphasis is directed more to physical intentions than to mathematical vigour. We start with a symplectic analysis of staties. Both discrete and continuous systems are considered on a largely intuitive level. The notion of reciprocity and potentiality of the theory is discussed. Chapter II is a presentation of particle dynamics together with more rigorous definitions of the geometric structure. Lagrangian-Submanifolds and their generating function 3 are defined and the time evolution of particle states is studied. Chapter II form the main part of these notes. Here we describe the construction of canonical momenta and discuss the field dynamics in finite domains of space-time. We also establish the relation between our symplectic framework and the geometric formulation of the calculus of variations of multiple integrals. In the following chapter we give a few examples of field theories selected to illustrate various features of the new approach. A new formulation of the theory of gravity consists of using the affine connection in space-time as the field configuration. In the past section we present an analysis of hydrodynamics within our framework which reveals a formal analogy with electrodynamics. The discovery of potentials for hydrodynamics and the subsequent formulation of a variational principle provides an excellent example for the fruitfulness of the new approach to field theory. A short review of

  7. Theoretical physics. Field theory

    International Nuclear Information System (INIS)

    Landau, L.; Lifchitz, E.

    2004-01-01

    This book is the fifth French edition of the famous course written by Landau/Lifchitz and devoted to both the theory of electromagnetic fields and the gravity theory. The talk of the theory of electromagnetic fields is based on special relativity and relates to only the electrodynamics in vacuum and that of pointwise electric charges. On the basis of the fundamental notions of the principle of relativity and of relativistic mechanics, and by using variational principles, the authors develop the fundamental equations of the electromagnetic field, the wave equation and the processes of emission and propagation of light. The theory of gravitational fields, i.e. the general theory of relativity, is exposed in the last five chapters. The fundamentals of the tensor calculus and all that is related to it are progressively introduced just when needed (electromagnetic field tensor, energy-impulse tensor, or curve tensor...). The worldwide reputation of this book is generally allotted to clearness, to the simplicity and the rigorous logic of the demonstrations. (A.C.)

  8. Quantum field theory

    CERN Document Server

    Sadovskii, Michael V

    2013-01-01

    This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive approach allows a deep understanding of ideas and methods used for solving problems in this field.

  9. Conformal field theory in conformal space

    International Nuclear Information System (INIS)

    Preitschopf, C.R.; Vasiliev, M.A.

    1999-01-01

    We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d + 2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d = (1, 3) and any standard matter coupled to it. An important feature is the automatic derivation of the conformal gravity constraints, which are necessary for the analysis of the matter systems

  10. Simple recursion relations for general field theories

    International Nuclear Information System (INIS)

    Cheung, Clifford; Shen, Chia-Hsien; Trnka, Jaroslav

    2015-01-01

    On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.

  11. Gauge field theories

    International Nuclear Information System (INIS)

    Leite Lopes, J.

    1981-01-01

    The book is intended to explain, in an elementary way, the basic notions and principles of gauge theories. Attention is centred on the Salem-Weinberg model of electro-weak interactions, as well as neutrino-lepton scattering and the parton model. Classical field theory, electromagnetic, Yang-Mills and gravitational gauge fields, weak interactions, Higgs mechanism and the SU(5) model of grand unification are also discussed. (U.K.)

  12. Supersymmetric gauge field theories

    International Nuclear Information System (INIS)

    Slavnov, A.A.

    1976-01-01

    The paper is dealing with the role of supersymmetric gauge theories in the quantum field theory. Methods of manipulating the theories as well as possibilities of their application in elementary particle physics are presented. In particular, the necessity is explained of a theory in which there is symmetry between Fermi and Bose fields, in other words, of the supersymmetric gauge theory for construction of a scheme for the Higgs particle connecting parameters of scalar mesons with those of the rest fields. The mechanism of supersymmetry breaking is discussed which makes it possible to remain the symmetric procedure of renormalization intact. The above mechanism of spontaneous symmetry breaking is applied to demonstrate possibilities of constructing models of weak and electromagnetic interactions which would be acceptable from the point of view of experiments. It is noted that the supersymmetric gauge theories represent a natural technique for description of vector-like models

  13. Quantum field theory of fluids.

    Science.gov (United States)

    Gripaios, Ben; Sutherland, Dave

    2015-02-20

    The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.

  14. Modular groups in quantum field theory

    International Nuclear Information System (INIS)

    Borchers, H.-J.

    2000-01-01

    The author discusses the connection of Lagrangean quantum field theory, perturbation theory, the Lehmann-Symanzik-Zimmermann theory, Wightman's quantum field theory, the Euclidean quantum field theory, and the Araki-Haag-Kastler theory of local observables with modular groups. In this connection he considers the PCT-theorem, and the tensor product decomposition. (HSI)

  15. Introduction to conformal field theory. With applications to string theory

    International Nuclear Information System (INIS)

    Blumenhagen, Ralph; Plauschinn, Erik

    2009-01-01

    Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields. (orig.)

  16. Gauge field theories

    International Nuclear Information System (INIS)

    Pokorski, S.

    1987-01-01

    Quantum field theory forms the present theoretical framework for the understanding of the fundamental interactions of particle physics. This book examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. The author discusses field-theoretical techniques and encourages the reader to perform many of the calculations presented. This book includes a brief introduction to perturbation theory, the renormalization programme, and the use of the renormalization group equation. Several topics of current research interest are covered, including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry

  17. Grand partition function in field theory with applications to sine-Gordon field theory

    International Nuclear Information System (INIS)

    Samuel, S.

    1978-01-01

    Certain relativistic field theories are shown to be equivalent to the grand partition function of an interacting gas. Using the physical insight given by this analogy many field-theoretic results are obtained, particularly for the sine-Gordon field theory. The main results are enumerated in the summary to which the reader is referred

  18. String field theory-inspired algebraic structures in gauge theories

    International Nuclear Information System (INIS)

    Zeitlin, Anton M.

    2009-01-01

    We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.

  19. Covariant Noncommutative Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)

    2008-07-02

    The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.

  20. Covariant Noncommutative Field Theory

    International Nuclear Information System (INIS)

    Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

    2008-01-01

    The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced

  1. [Studies in quantum field theory

    International Nuclear Information System (INIS)

    1990-01-01

    During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity

  2. Perturbation theory for quantized string fields

    International Nuclear Information System (INIS)

    Thorn, C.B.; Florida Univ., Gainesville

    1987-01-01

    We discuss the problem of gauge fixing in string field theory. We show that BRST invariance requires the gauge-fixed action to contain terms cubic in the ghost... of ghost of ghost fields. The final BRST invariant gauge-fixed action for the gauge b 0 A=0 is extremely simple: with the proper interpretation (as given in this article), it is essentially the one anticipated earlier in the work of Giddings, Martinec, and Witten in their analysis of the BRST invariant world-sheet approach to string theory. We derive the Feynman rules from this action and explain in detail how the sum over sufaces of the BRST first-quantized string is reproduced. This result depends crucially on the correct assignment for the Grassmann character of the string field and its ghost... of ghost of ghost string fields. If all these fields are unified in a single string field Φ containing all ghost numbers, the requirements is that Φ be uniformly Grassmann odd. Finally, we do some sample calculations which provide some simple checks on our general results. (orig.)

  3. Affine field theories

    International Nuclear Information System (INIS)

    Cadavid, A.C.

    1989-01-01

    The author constructs a non-Abelian field theory by gauging a Kac-Moody algebra, obtaining an infinite tower of interacting vector fields and associated ghosts, that obey slightly modified Feynman rules. She discusses the spontaneous symmetry breaking of such theory via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra. She proceeds to show that there is no obstacle in implementing the affine extension of supersymmetric Yang-Mills theories. The result is valid in four, six and ten space-time dimensions. Then the affine extension of supergravity is investigated. She discusses only the loop algebra since the affine extension of the super-Poincare algebra appears inconsistent. The construction of the affine supergravity theory is carried out by the group manifold method and leads to an action describing infinite towers of spin 2 and spin 3/2 fields that interact subject to the symmetries of the loop algebra. The equations of motion satisfy the usual consistency check. Finally, she postulates a theory in which both the vector and scalar fields lie in the loop algebra of SO(3). This theory has an expanded soliton sector, and corresponding to the original 't Hooft-Polyakov solitonic solutions she now finds an infinite family of exact, special solutions of the new equations. She also proposes a perturbation method for obtaining an arbitrary solution of those equations for each level of the affine index

  4. Features of finite quantum field theories

    International Nuclear Information System (INIS)

    Boehm, M.; Denner, A.

    1987-01-01

    We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)

  5. WORKSHOP: Thermal field theory

    Energy Technology Data Exchange (ETDEWEB)

    Anon.

    1989-04-15

    The early history of the Universe is a crucial testing ground for theories of elementary particles. Speculative ideas about the constituents of matter and their interactions are reinforced if they are consistent with what we suppose happened near the beginning of time and discarded if they are not. The cosmological consequences of these theories are usually deduced using a general statistical approach called thermal field theory. Thus, 75 physicists from thirteen countries met in Cleveland, Ohio, last October for the first 'Workshop on Thermal Field Theories and their Applications'.

  6. Quantum groups, quantum categories and quantum field theory

    CERN Document Server

    Fröhlich, Jürg

    1993-01-01

    This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.

  7. Finite quantum field theories

    International Nuclear Information System (INIS)

    Lucha, W.; Neufeld, H.

    1986-01-01

    We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)

  8. Quantum Yang-Mills theory of Riemann surfaces and conformal field theory

    International Nuclear Information System (INIS)

    Killingback, T.P.

    1989-01-01

    It is shown that Yang-Mills theory on a smooth surface, when suitably quantized, is a topological quantum field theory. This topological gauge theory is intimately related to two-dimensional conformal field theory. It is conjectured that all conformal field theories may be obtained from Yang-Mills theory on smooth surfaces. (orig.)

  9. M Theory on AdSp x S11-p and superconformal field theories

    International Nuclear Information System (INIS)

    Aharony, Ofer; Yaron, Oz; Zheng, Yin

    1998-01-01

    We study the large N limit of the interacting superconformal field theories associated with N M5 branes or M2 branes using the recently proposed relation between these theories and M theory on AdS spaces. We first analyze the spectrum of chiral operators of the 6d (0, 2) theory associated with M5 branes in flat space, and find full agreement with earlier results obtained using its DLCQ description as quantum mechanics on a moduli space of instantons. We then perform a similar analysis for the D N type 6d (0, 2) theories associated with M5 branes at an R 5 /Z 2 singularity, and for the 3d N = 8 superconformal field theories associated with M2 branes in flat space and at an R 8 /Z 2 singularity respectively. Little is known about these three theories, and our study yields for the first time their spectrum of chiral operators (in the large N limit)

  10. Phase space properties of charged fields in theories of local observables

    International Nuclear Information System (INIS)

    Buchholz, D.; D'Antoni, C.

    1994-10-01

    Within the setting of algebraic quantum field theory a relation between phase-space properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclarity conditions which are the basis for the characterization of theories with physically reasonable causal and thermal features. Relevant concepts and results of phase space analysis in algebraic qunatum field theory are reviewed and the underlying ideas are outlined. (orig.)

  11. A superstring field theory for supergravity

    Science.gov (United States)

    Reid-Edwards, R. A.; Riccombeni, D. A.

    2017-09-01

    A covariant closed superstring field theory, equivalent to classical tendimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the NeveuSchwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.

  12. Quantum Field Theory A Modern Perspective

    CERN Document Server

    Parameswaran Nair, V

    2005-01-01

    Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...

  13. Noncommutative field theory

    International Nuclear Information System (INIS)

    Douglas, Michael R.; Nekrasov, Nikita A.

    2001-01-01

    This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level

  14. Perturbation theory at large order in more than one coupling constant for a field theory with fermions

    International Nuclear Information System (INIS)

    Chowdhury, A.R.; Roy, T.

    1980-01-01

    We have considered the problem of evaluating the large order estimates of perturbation theory in a quantum field theory with more than one coupling constant. The theory considered is four dimensional and possesses instanton-type solutions. It contains a Boson field coupled with a Fermion through the usual g anti psi psi phi type interaction, along with the self-interaction of the Boson lambda phi 4 . Our analysis reveals a phenomenon not observed in a theory with only one coupling constant. One gets different kinds of behavior in different regions of the (lambda, g) plane. The results are quite encouraging for the application to more realistic field theories

  15. Aspects of affine Toda field theory

    International Nuclear Information System (INIS)

    Braden, H.W.; Corrigan, E.; Dorey, P.E.; Sasaki, R.

    1990-05-01

    The report is devoted to properties of the affine Toda field theory, the intention being to highlight a selection of curious properties that should be explicable in terms of the underlying group theory but for which in most cases there are no explanation. The motivation for exploring the ideas contained in this report came principally from the recent work of Zamolodchikov concerning the two dimensional Ising model at critical temperature perturbed by a magnetic field. Hollowood and Mansfield pointed out that since Toda field theory is conformal the perturbation considered by Zamolodchikov might well be best regarded as a perturbation of a Toda field theory. This work made it seem plausible that the theory sought by Zamolodchikov was actually affine E 8 Toda field theory. However, this connection required an imaginary value of the coupling constant. Investigations here concerning exact S-matrices use a perturbative approach based on real coupling and the results differ in various ways from those thought to correspond to perturbed conformal field theory. A further motivation is to explore the connection between conformal and perturbed conformal field theories in other contexts using similar ideas. (N.K.)

  16. Towards weakly constrained double field theory

    Directory of Open Access Journals (Sweden)

    Kanghoon Lee

    2016-08-01

    Full Text Available We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.

  17. Topics in low-dimensional field theory

    International Nuclear Information System (INIS)

    Crescimanno, M.J.

    1991-01-01

    Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density

  18. Nonequilibrium quantum field theories

    International Nuclear Information System (INIS)

    Niemi, A.J.

    1988-01-01

    Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena. (orig.)

  19. Quantum field theory with infinite component local fields as an alternative to the string theories

    International Nuclear Information System (INIS)

    Krasnikov, N.V.

    1987-05-01

    We show that the introduction of the infinite component local fields with higher order derivatives in the interaction makes the theory completely ultraviolet finite. For the γ 5 -anomalous theories the introduction of the infinite component field makes the theory renormalizable or superrenormalizable. (orig.)

  20. Hyperfunction quantum field theory

    International Nuclear Information System (INIS)

    Nagamachi, S.; Mugibayashi, N.

    1976-01-01

    The quantum field theory in terms of Fourier hyperfunctions is constructed. The test function space for hyperfunctions does not contain C infinitely functios with compact support. In spite of this defect the support concept of H-valued Fourier hyperfunctions allows to formulate the locality axiom for hyperfunction quantum field theory. (orig.) [de

  1. Correspondence between quantum gauge theories without ghost fields and their covariantly quantized theories with ghost fields

    International Nuclear Information System (INIS)

    Cheng Hung; Tsai Ercheng

    1986-01-01

    We give a correspondence formula which equates transition amplitudes in a quantum gauge field theory without ghost fields to those in a quantum theory with the gauge fields covariantly quantized and coupled to ghost fields. (orig.)

  2. The logarithmic conformal field theories

    International Nuclear Information System (INIS)

    Rahimi Tabar, M.R.; Aghamohammadi, A.; Khorrami, M.

    1997-01-01

    We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two- and three-point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any n-point function containing the logarithmic field in terms of ordinary n-point functions. Finally, we calculate the operator product expansion (OPE) coefficients of a logarithmic conformal field theory, and show that these can be obtained from the corresponding coefficients of ordinary conformal theory by a simple derivation. (orig.)

  3. 1. Vienna central european seminar on particle physics and quantum field theory. Advances in quantum field theory. Program

    International Nuclear Information System (INIS)

    Hueffel, H.

    2004-01-01

    The new seminar series 'Vienna central European seminar on particle physics and quantum field theory' has been created 2004 and is intended to provide interactions between leading researchers and junior physicists. This year 'Advances in quantum field theory' has been chosen as subject and is centred on field theoretic aspects of string dualities. The lectures mainly focus on these aspects of string dualities. Further lectures regarding supersymmetric gauge theories, quantum gravity and noncommutative field theory are presented. The vast field of research concerning string dualities justifies special attention to their effects on field theory. (author)

  4. Causality Constraints in Conformal Field Theory

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d-dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinni...

  5. Causality constraints in conformal field theory

    Energy Technology Data Exchange (ETDEWEB)

    Hartman, Thomas; Jain, Sachin; Kundu, Sandipan [Department of Physics, Cornell University,Ithaca, New York (United States)

    2016-05-17

    Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ϕ){sup 4} coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.

  6. (Non-)decoupled supersymmetric field theories

    International Nuclear Information System (INIS)

    Pietro, Lorenzo Di; Dine, Michael; Komargodski, Zohar

    2014-01-01

    We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS 4 Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)

  7. Bell-type quantum field theories

    International Nuclear Information System (INIS)

    Duerr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghi, Nino

    2005-01-01

    In his paper (1986 Beables for quantum field theory Phys. Rep. 137 49-54) John S Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a vertical bar Ψ vertical bar 2 -distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; we call such processes Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to 'second quantization'. As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (topical review)

  8. BRST field theory of relativistic particles

    International Nuclear Information System (INIS)

    Holten, J.W. van

    1992-01-01

    A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. The authors discuss their quantization, gauge fixing and the derivation of propagators. It is shown, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same phenomenon holds in string theories. In particular it is shown, that the naive BRST formulation of the BDHP theory leads to trivial quantum field theories with vanishing correlation functions. (author). 22 refs

  9. On spin chains and field theories

    International Nuclear Information System (INIS)

    Roiban, Radu

    2004-01-01

    We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory whose 1-loop scale transformations are generated by the spin chain hamiltonian. We also identify a necessary condition for a given field theory to be related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalization of the XXZ Heisenberg spin chain and its associated field theory. The system has no nonabelian global symmetries and generally does not admit a supersymmetric extension without the introduction of more propagating bosonic fields. For the case of a 2-state chain we find the spectrum and the eigenstates. For certain values of its coupling constants the field theory associated to this general type of chain is the bosonic sector of the q-deformation of N = 4 SYM theory. (author)

  10. Gauge field theory

    International Nuclear Information System (INIS)

    Aref'eva, I.Ya.; Slavnov, A.A.

    1981-01-01

    This lecture is devoted to the discussion of gauge field theory permitting from the single point of view to describe all the interactions of elementary particles. The authors used electrodynamics and the Einstein theory of gravity to search for a renormgroup fixing a form of Lagrangian. It is shown that the gauge invariance added with the requirement of the minimum number of arbitraries in Lagrangian fixes unambigously the form of the electromagnetic interaction. The generalization of this construction for more complicate charge spaces results in the Yang-Mills theory. The interaction form in this theory is fixed with the relativity principle in the charge space. A quantum scheme of the Yang-Mills fields through the explicit separation of true dynamic variables is suggested. A comfortable relativistically invariant diagram technique for the calculation of a producing potential for the Green functions is described. The Ward generalized identities have been obtained and a procedure of the elimination of ultraviolet and infrared divergencies has been accomplished. Within the framework of QCD (quantum-chromodynamic) the phenomenon of the asymptotic freedom being the most successful prediction of the gauge theory of strong interactions was described. Working methods with QCD outside the framework of the perturbation theory have been described from a coupling constant. QCD is represented as a single theory possessing both the asymptotical freedom and the freedom retaining quarks [ru

  11. Time independent mean-field theory

    International Nuclear Information System (INIS)

    Negele, J.W.

    1980-02-01

    The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures

  12. Interpolating string field theories

    International Nuclear Information System (INIS)

    Zwiebach, B.

    1992-01-01

    This paper reports that a minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles

  13. Finite temperature field theory

    CERN Document Server

    Das, Ashok

    1997-01-01

    This book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are al

  14. Wavelet-Based Quantum Field Theory

    Directory of Open Access Journals (Sweden)

    Mikhail V. Altaisky

    2007-11-01

    Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.

  15. Algebraic quantum field theory

    International Nuclear Information System (INIS)

    Foroutan, A.

    1996-12-01

    The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)

  16. On the background independence of string field theory

    International Nuclear Information System (INIS)

    Sen, A.

    1990-01-01

    Given a solution Ψ cl of the classical equations of motion in either closed or open string field theory formulated around a given conformal field theory background, we can construct a new operator Q B in the corresponding two-dimensional field theory such that (Q B ) 2 =0. It is shown that in the limit when the background field Ψ cl is weak, Q B can be identified with the BRST charge of a new local conformal field theory. This indicates that the string field theories formulated around these two different conformal field theories are actually the same theory, and that these two conformal field theories may be regarded as different classical solutions of this string field theory. (orig.)

  17. Supersymmetric extensions of K field theories

    Science.gov (United States)

    Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.

    2012-02-01

    We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.

  18. Quantum field theory in gravitational background

    International Nuclear Information System (INIS)

    Narnhofer, H.

    1986-01-01

    The author suggests ignoring the influence of the quantum field on the gravitation as the first step to combine quantum field theory and gravitation theory, but to consider the gravitational field as fixed and thus study quantum field theory on a manifold. This subject evoked interest when thermal radiation of a black hole was predicted. The author concentrates on the free quantum field and can split the problem into two steps: the Weyl-algebra of the free field and the Wightman functional on the tangent space

  19. Blockspin transformations for finite temperature field theories with gauge fields

    International Nuclear Information System (INIS)

    Kerres, U.

    1996-08-01

    A procedure is proposed to study quantum field theories at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices. The ultimate aim is to compute constraint effective potentials, i.e. the free energy as a function of suitable order parameters. From the free energy one can read off the thermodynamic behaviour of the theory, in particular the existence and nature of phase transitions. In a finite temperature field theory one begins with either one or a sequence of transformations which transform the original theory into an effective theory on a three-dimensional lattice. Its effective action has temperature dependent coefficients. Thereafter one may proceed with further blockspin transformations of the three-dimensional theory. Assuming a finite volume, this can in principle be continued until one ends with a lattice with a single site. Its effective action is the constraint effective potential. In each RG-step, an integral over the high frequency part of the field, also called the fluctuation field, has to be performed. This is done by perturbation theory. It requires the knowledge of bare fluctuation field propagators and of interpolation operators which enter into the vertices. A detailed examination of these quantities is presented for scalar fields, abelian gauge fields and for Higgs fields, finite temperature is admitted. The lattice perturbation theory is complicated because the bare lattice propagators are complicated. This is due to a partial loss of translation invariance in each step. Therefore the use of translation invariant cutoffs in place of a lattice is also discussed. In case of gauge fields this is only possible as a continuum version of the blockspin method. (orig.)

  20. Introduction to quantum field theory

    CERN Document Server

    Alvarez-Gaumé, Luís

    1994-01-01

    The purpose of this lecture is to review some elementary aspects of Quantum Field Theory. From the necessity to introduce quantum fields once quantum mechanics and special relativity are put together, to some of the basic practical computational tools in the subject, including the canonical quantization of simple field theories, the derivation of Feynman rules, computation of cross sections and decay rates, some introductory remarks on the treatment of unstable states and the possible realization of symmetries in a general field theory. The audience is required to have a working knowledge of quantum mechanics and special relativity and it would also be desirable to know the rudiments of relativistic quantum mechanics.

  1. Conformal techniques in string theory and string field theory

    International Nuclear Information System (INIS)

    Giddings, S.B.

    1987-01-01

    The application of some conformal and Riemann surface techniques to string theory and string field theory is described. First a brief review of Riemann surface techniques and of the Polyakov approach to string theory is presented. This is followed by a discussion of some features of string field theory and of its Feynman rules. Specifically, it is shown that the Feynman diagrams for Witten's string field theory respect modular invariance, and in particular give a triangulation of moduli space. The Polyakov formalism is then used to derive the Feynman rules that should follow from this theory upon gauge-fixing. It should also be possible to apply this derivation to deduce the Feynman rules for other gauge-fixed string field theories. Following this, Riemann surface techniques are turned to the problem of proving the equivalence of the Polyakov and light-cone formalisms. It is first shown that the light-cone diagrams triangulate moduli space. Then the Polyakov measure is worked out for these diagrams, and shown to equal that deduced from the light-cone gauge fixed formalism. Also presented is a short description of the comparison of physical states in the two formalisms. The equivalence of the two formalisms in particular constitutes a proof of the unitarity of the Polyakov framework for the closed bosonic string

  2. Superconformal quantum field theories in string. Gauge theory dualities

    Energy Technology Data Exchange (ETDEWEB)

    Wiegandt, Konstantin

    2012-08-14

    In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

  3. Superconformal quantum field theories in string. Gauge theory dualities

    International Nuclear Information System (INIS)

    Wiegandt, Konstantin

    2012-01-01

    In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

  4. Mathematical aspects of quantum field theory

    CERN Document Server

    de Faria, Edson

    2010-01-01

    Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

  5. Closed string field theory

    International Nuclear Information System (INIS)

    Strominger, A.

    1987-01-01

    A gauge invariant cubic action describing bosonic closed string field theory is constructed. The gauge symmetries include local spacetime diffeomorphisms. The conventional closed string spectrum and trilinear couplings are reproduced after spontaneous symmetry breaking. The action S is constructed from the usual ''open string'' field of ghost number minus one half. It is given by the associator of the string field product which is non-vanishing because of associativity anomalies. S does not describe open string propagation because open string states associate and can thereby be shifted away. A field theory of closed and open strings can be obtained by adding to S the cubic open string action. (orig.)

  6. Fermion boson metamorphosis in field theory

    International Nuclear Information System (INIS)

    Ha, Y.K.

    1982-01-01

    In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered

  7. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian gauge theories, and gravitation. 3. ed.

    International Nuclear Information System (INIS)

    Scheck, Florian

    2010-01-01

    Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [de

  8. The Global Approach to Quantum Field Theory

    International Nuclear Information System (INIS)

    Folacci, Antoine; Jensen, Bruce

    2003-01-01

    is rather difficult to read because of its great breadth. From the start he is faithful to his own view of field theory by developing a powerful formalism which permits him to discuss broad general features common to all field theories. He demands a considerable effort from the reader to penetrate his formalism, and a reading of Appendix A which presents the basics of super-analysis is a prerequisite. To keep the reader on course, DeWitt offers a series of exercises on applications of global formalism in Part 8, nearly 200 pages worth. The exercises are to be worked in parallel with reading the text, starting from the beginning. Before concluding, some criticisms. DeWitt has anticipated some criticism himself in the Preface, where he warns the reader that 'this book is in no sense a reference book on quantum field theory and its application to particle physics. The selection of topics is idiosyncratic. But the reviewers should add a few more remarks: (1) There are very few references. Of course, this is because the work is largely original. Even where the work of other researchers is presented, it has mostly been transformed by the DeWittian point of view. (2) There are very few diagrams, which sometimes hinders the exposition. In summary, in our opinion, this is one of the best books dealing with quantum field theory existing today. It will be of great interest for graduate and postgraduate students as well as workers in the domains of quantum field theory in flat and in curved spacetime and string theories. But we believe that the reader must have previously studied standard textbooks on quantum field theory and general relativity. Even with this preparation, it is by no means an easy book to read. However, the reward is to be able to share the deep and unique vision of the quantum theory of fields and its formalism by one of its greatest expositors. (book review)

  9. N=1 field theory duality from M theory

    International Nuclear Information System (INIS)

    Schmaltz, M.; Sundrum, R.

    1998-01-01

    We investigate Seiberg close-quote s N=1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in type IIA string theory is given an elegant derivation from M theory. copyright 1998 The American Physical Society

  10. (Non-)decoupled supersymmetric field theories

    Energy Technology Data Exchange (ETDEWEB)

    Pietro, Lorenzo Di [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel); Dine, Michael [Santa Cruz Institute for Particle Physics and Department of Physics,Santa Cruz CA 95064 (United States); Komargodski, Zohar [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel)

    2014-04-10

    We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS{sub 4} Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)

  11. Conformal generally covariant quantum field theory. The scalar field and its Wick products

    Energy Technology Data Exchange (ETDEWEB)

    Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2008-06-15

    In this paper we generalize the construction of generally covariant quantum theories given in [R. Brunetti, K. Fredenhagen, R. Verch, Commun. Math. Phys. 237, 31 (2003)] to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale {mu} appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields. (orig.)

  12. Conformal generally covariant quantum field theory. The scalar field and its Wick products

    International Nuclear Information System (INIS)

    Pinamonti, N.

    2008-06-01

    In this paper we generalize the construction of generally covariant quantum theories given in [R. Brunetti, K. Fredenhagen, R. Verch, Commun. Math. Phys. 237, 31 (2003)] to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale μ appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields. (orig.)

  13. Families and degenerations of conformal field theories

    Energy Technology Data Exchange (ETDEWEB)

    Roggenkamp, D.

    2004-09-01

    In this work, moduli spaces of conformal field theories are investigated. In the first part, moduli spaces corresponding to current-current deformation of conformal field theories are constructed explicitly. For WZW models, they are described in detail, and sigma model realizations of the deformed WZW models are presented. The second part is devoted to the study of boundaries of moduli spaces of conformal field theories. For this purpose a notion of convergence of families of conformal field theories is introduced, which admits certain degenerated conformal field theories to occur as limits. To such a degeneration of conformal field theories, a degeneration of metric spaces together with additional geometric structures can be associated, which give rise to a geometric interpretation. Boundaries of moduli spaces of toroidal conformal field theories, orbifolds thereof and WZW models are analyzed. Furthermore, also the limit of the discrete family of Virasoro minimal models is investigated. (orig.)

  14. Dynamical Mean Field Approximation Applied to Quantum Field Theory

    CERN Document Server

    Akerlund, Oscar; Georges, Antoine; Werner, Philipp

    2013-12-04

    We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...

  15. Field theory approach to gravitation

    International Nuclear Information System (INIS)

    Yilmaz, H.

    1978-01-01

    A number of authors considered the possibility of formulating a field-theory approach to gravitation with the claim that such an approach would uniquely lead to Einstein's theory of general relativity. In this article it is shown that the field theory approach is more generally applicable and uniqueness cannot be claimed. Theoretical and experimental reasons are given showing that the Einsteinian limit appears to be unviable

  16. Dualities among one-time field theories with spin, emerging from a unifying two-time field theory

    International Nuclear Information System (INIS)

    Bars, Itzhak; Quelin, Guillaume

    2008-01-01

    The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS d-k xS k , and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure

  17. Mathematical aspects of quantum field theories

    CERN Document Server

    Strobl, Thomas

    2015-01-01

    Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...

  18. Introduction to quantum field theory

    International Nuclear Information System (INIS)

    Kazakov, D.I.

    1988-01-01

    The lectures appear to be a continuation to the introduction to elementary principles of the quantum field theory. The work is aimed at constructing the formalism of standard particle interaction model. Efforts are made to exceed the limits of the standard model in the quantum field theory context. Grand unification models including strong and electrical weak interactions, supersymmetric generalizations of the standard model and grand unification theories and, finally, supergravitation theories including gravitation interaction to the universal scheme, are considered. 3 refs.; 19 figs.; 2 tabs

  19. Vertex operator algebras and conformal field theory

    International Nuclear Information System (INIS)

    Huang, Y.Z.

    1992-01-01

    This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics

  20. A landscape of field theories

    Energy Technology Data Exchange (ETDEWEB)

    Maxfield, Travis [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States); Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843-4242 (United States); Sethi, Savdeep [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States)

    2016-11-28

    Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2,0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.

  1. Effective field theory of cosmological perturbations

    International Nuclear Information System (INIS)

    Piazza, Federico; Vernizzi, Filippo

    2013-01-01

    The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu–Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy. (paper)

  2. Effective field theory of cosmological perturbations

    Science.gov (United States)

    Piazza, Federico; Vernizzi, Filippo

    2013-11-01

    The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.

  3. Boundary effects on quantum field theories

    International Nuclear Information System (INIS)

    Lee, Tae Hoon

    1991-01-01

    Quantum field theory in the S 1 *R 3 space-time is simply described by the imaginary time formalism. We generalize Schwinger-DeWitt proper-time technique which is very useful in zero temperature field theories to this case. As an example we calculate the one-loop effective potential of the finite temperature scala field theory by this technique.(Author)

  4. Generalized Field Theory and Kasner universe

    International Nuclear Information System (INIS)

    Klotz, A.H.

    1986-01-01

    It is shown that the only Kasner-like solution of the Generalized Field Theory field equations with a nonzero electromagnetic field corresponds to an empty field geometry of the space-time. In this case, the electromagnetic field tensors of the theory coincide as could be expected from general considerations. 6 refs. (author)

  5. The Global Approach to Quantum Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Folacci, Antoine; Jensen, Bruce [Faculte des Sciences, Universite de Corse (France); Department of Mathematics, University of Southampton (United Kingdom)

    2003-12-12

    be noted that DeWitt's book is rather difficult to read because of its great breadth. From the start he is faithful to his own view of field theory by developing a powerful formalism which permits him to discuss broad general features common to all field theories. He demands a considerable effort from the reader to penetrate his formalism, and a reading of Appendix A which presents the basics of super-analysis is a prerequisite. To keep the reader on course, DeWitt offers a series of exercises on applications of global formalism in Part 8, nearly 200 pages worth. The exercises are to be worked in parallel with reading the text, starting from the beginning. Before concluding, some criticisms. DeWitt has anticipated some criticism himself in the Preface, where he warns the reader that 'this book is in no sense a reference book on quantum field theory and its application to particle physics. The selection of topics is idiosyncratic. (book review)[abstract truncated

  6. On finite quantum field theories

    International Nuclear Information System (INIS)

    Rajpoot, S.; Taylor, J.G.

    1984-01-01

    The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)

  7. Quantum Field Theory

    CERN Document Server

    Zeidler, Eberhard

    This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from othe...

  8. Microcontinuum field theories

    CERN Document Server

    Eringen, A Cemal

    1999-01-01

    Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. Material bodies are here viewed as collections of large numbers of deformable particles, much as each volume element of a fluid in statistical mechanics is viewed as consisting of a large number of small particles for which statistical laws are valid. Classical continuum theories are valid when the characteristic length associated with external forces or stimuli is much larger than any internal scale of the body under consideration. When the characteristic lengths are comparable, however, the response of the individual constituents becomes important, for example, in considering the fluid or elastic properties of blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balanc...

  9. Introduction to algebraic quantum field theory

    International Nuclear Information System (INIS)

    Horuzhy, S.S.

    1990-01-01

    This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs

  10. Quaternionic quantum field theory

    International Nuclear Information System (INIS)

    Adler, S.L.

    1986-01-01

    In this paper the author describes a new kind of quantum mechanics or quantum field theory based on quaternions. Quaternionic quantum mechanics has a Schrodinger equation, a Dirac transformation theory, and a functional integral. Quaternionic quantum mechanics does not seem to have (except in the complex quantum mechanics specialization): A correspondence principle, and beyond this a commuting tensor product, asymptotic states, an S-matrix, a canonical formalism, coherent states or a Euclidean continuation. A new kind of quantum mechanics exists. There are many interesting formal questions to study, which should enable one to decide whether quaternionic quantum field theory is relevant for particle physics

  11. A philosophical approach to quantum field theory

    CERN Document Server

    Öttinger, Hans Christian

    2015-01-01

    This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics, and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather than a formal understanding.

  12. Toward finite quantum field theories

    International Nuclear Information System (INIS)

    Rajpoot, S.; Taylor, J.G.

    1986-01-01

    The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)

  13. Superspace conformal field theory

    Energy Technology Data Exchange (ETDEWEB)

    Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-07-15

    Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.

  14. Superspace conformal field theory

    International Nuclear Information System (INIS)

    Quella, Thomas

    2013-07-01

    Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.

  15. Mean-field theory and solitonic matter

    International Nuclear Information System (INIS)

    Cohen, T.D.

    1989-01-01

    Finite density solitonic matter is considered in the context of quantum field theory. Mean-field theory, which provides a reasonable description for single-soliton properties gives rise to a crystalline description. A heuristic description of solitonic matter is given which shows that the low-density limit of solitonic matter (the limit which is presumably relevant for nuclear matter) does not commute with the mean-field theory limit and gives rise to a Fermi-gas description of the system. It is shown on the basis of a formal expansion of simple soliton models in terms of the coupling constant why one expects mean-field theory to fail at low densities and why the corrections to mean-field theory are nonperturbative. This heuristic description is tested against an exactly solvable 1+1 dimensional model (the sine-Gordon model) and found to give the correct behavior. The relevance of these results to the program of doing nuclear physics based on soliton models is discussed. (orig.)

  16. Lectures on matrix field theory

    CERN Document Server

    Ydri, Badis

    2017-01-01

    These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.

  17. Non-perturbative field theory/field theory on a lattice

    International Nuclear Information System (INIS)

    Ambjorn, J.

    1988-01-01

    The connection between the theory of critical phenomena in statistical mechanics and the renormalization of field theory is briefly outlined. The way of using this connection is described to get information about non-perturbative quantities in QCD and about more intelligent ways of doing the Monte Carlo (MC) simulations. The (MC) method is shown to be a viable one in high energy physics, but it is not a good substitute for an analytic understanding. MC-methods will be very valuable both for getting out hard numbers and for testing the correctness of new ideas

  18. Topics in phase-shift analysis and higher spin field theory

    International Nuclear Information System (INIS)

    Reisen, J.C.J.M.

    1983-01-01

    The first part of this thesis considers several aspects of the existence of phase-shift ambiguities. The subject is introduced with a few remarks on scattering theory and previous work in this area is discussed. The mathematical restrictions of presenting such problems clearly are considered and the construction of different unitary amplitudes which correspond to the same differential cross section is described. So far, examples of phase-shift ambiguities have only been found for rather special cases but the author shows that these results can be considerably generalized for spinless elastic scattering, leading to properties of phase-shift ambiguities being revealed that were previously absent. These properties are discussed in detail. Phase-shift ambiguities for the spin-0-spin-1/2 elastic scattering are then considered and again generalized. The second part of this thesis is concerned with the investigation of a free field theory for both massive and massless particles with higher spin (1, 2 and 3). A root method has been used which is described and shown to lead to the free field equations and the subsidiary conditions. A field equation and Lagrangian are constructed for massive particles and the former is then used to derive a massless field equation and Lagrangian. The relation between massive and massless field equations is investigated in more detail and particularly the expressions for the amplitude describing exchange of a particle between two external sources are compared. (Auth./C.F.)

  19. Cutkosky rules for superstring field theory

    International Nuclear Information System (INIS)

    Pius, Roji; Sen, Ashoke

    2016-01-01

    Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.

  20. Self-consistent normal ordering of gauge field theories

    International Nuclear Information System (INIS)

    Ruehl, W.

    1987-01-01

    Mean-field theories with a real action of unconstrained fields can be self-consistently normal ordered. This leads to a considerable improvement over standard mean-field theory. This concept is applied to lattice gauge theories. First an appropriate real action mean-field theory is constructed. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean-field theory are derived. (author). 4 refs

  1. Effective Field Theory on Manifolds with Boundary

    Science.gov (United States)

    Albert, Benjamin I.

    In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.

  2. Z/NZ conformal field theories

    International Nuclear Information System (INIS)

    Degiovanni, P.

    1990-01-01

    We compute the modular properties of the possible genus-one characters of some Rational Conformal Field Theories starting from their fusion rules. We show that the possible choices of S matrices are indexed by some automorphisms of the fusion algebra. We also classify the modular invariant partition functions of these theories. This gives the complete list of modular invariant partition functions of Rational Conformal Field Theories with respect to the A N (1) level one algebra. (orig.)

  3. Relativistic quantum mechanics and introduction to field theory

    Energy Technology Data Exchange (ETDEWEB)

    Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica

    1996-12-01

    The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.

  4. Relativistic quantum mechanics and introduction to field theory

    International Nuclear Information System (INIS)

    Yndurain, F.J.

    1996-01-01

    The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources

  5. Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields

    International Nuclear Information System (INIS)

    Anco, Stephen C.

    2003-01-01

    A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here

  6. Group field theory with noncommutative metric variables.

    Science.gov (United States)

    Baratin, Aristide; Oriti, Daniele

    2010-11-26

    We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.

  7. Perturbation theory and coupling constant analyticity in two-dimensional field theories

    International Nuclear Information System (INIS)

    Simon, B.

    1973-01-01

    Conjectural material and results over a year old are presented in the discussion of perturbation theory and coupling constant analyticity in two-dimensional field theories. General properties of perturbation series are discussed rather than questions of field theory. The question is interesting for two reasons: First, one would like to understand why perturbation theory is such a good guide (to show that perturbation theory determines the theory in some way). Secondly, one hopes to prove that some or all of the theories are nontrivial. (U.S.)

  8. Gaussian processes and constructive scalar field theory

    International Nuclear Information System (INIS)

    Benfatto, G.; Nicolo, F.

    1981-01-01

    The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)

  9. Nonadiabatic theory of strong-field atomic effects under elliptical polarization

    International Nuclear Information System (INIS)

    Wang Xu; Eberly, J. H.

    2012-01-01

    Elliptically polarized laser fields provide a new channel for access to strong-field processes that are either suppressed or not present under linear polarization. Quantum theory is mostly unavailable for their analysis, and we report here results of a systematic study based on a classical ensemble theory with solution of the relevant ab inito time-dependent Newton equations for selected model atoms. The study's approach is necessarily nonadiabatic, as it follows individual electron trajectories leading to single, double, and triple ionizations. Of particular interest are new results bearing on open questions concerning experimental reports of unexplained species dependences as well as double-electron release times that are badly matched by a conventional adiabatic quantum tunneling theory. We also report the first analysis of electron trajectories for sequential and non-sequential triple ionization.

  10. Semiclassical methods in field theories

    International Nuclear Information System (INIS)

    Ventura, I.

    1978-10-01

    A new scheme is proposed for semi-classical quantization in field theory - the expansion about the charge (EAC) - which is developed within the canonical formalism. This method is suitable for quantizing theories that are invariant under global gauge transformations. It is used in the treatment of the non relativistic logarithmic theory that was proposed by Bialynicki-Birula and Mycielski - a theory we can formulate in any number of spatial dimensions. The non linear Schroedinger equation is also quantized by means of the EAC. The classical logarithmic theories - both, the non relativistic and the relativistic one - are studied in detail. It is shown that the Bohr-Sommerfeld quantization rule(BSQR) in field theory is, in many cases, equivalent to charge quantization. This rule is then applied to the massive Thirring Model and the logarithmic theories. The BSQR can be see as a simplified and non local version of the EAC [pt

  11. Mean fields and self consistent normal ordering of lattice spin and gauge field theories

    International Nuclear Information System (INIS)

    Ruehl, W.

    1986-01-01

    Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)

  12. Algebraic quantum field theory, perturbation theory, and the loop expansion

    International Nuclear Information System (INIS)

    Duetsch, M.; Fredenhagen, K.

    2001-01-01

    The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)

  13. Singularity theory and N = 2 superconformal field theories

    International Nuclear Information System (INIS)

    Warner, N.P.

    1989-01-01

    The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs

  14. Meta fluid dynamic as a gauge field theory

    International Nuclear Information System (INIS)

    Mendes, A.C.R.; Neves, C.; Oliveira, W.; Takakura, F.I.

    2003-01-01

    In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the meta fluid dynamics, is extended in order to reformulate the meta fluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the meta fluid theory. Also, the geometrical interpretation to the gauge symmetries is discussed. (author)

  15. Higher-derivative boson field theories and constrained second-order theories

    Energy Technology Data Exchange (ETDEWEB)

    Urries, F.J. de [Departamento de Fisica, Universidad de Alcala de Henares, Madrid (Spain) and IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (Spain)]. E-mail: fernando.urries@uah.es; Julve, J. [IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (Spain)]. E-mail: julve@imaff.cfmac.csic.es; Sanchez, E.J. [IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (ES) and Departamento de Matematica, Universidad Europea, Madrid (Spain)]. E-mail: ejesus.sanchez@mat.ind.uem.es

    2001-10-26

    As an alternative to the covariant Ostrogradski method, we show that higher-derivative (HD) relativistic Lagrangian field theories can be reduced to second differential order by writing them directly as covariant two-derivative theories involving Lagrange multipliers and new fields. Despite the intrinsic non-covariance of the Dirac procedure used to deal with the constraints, the explicit Lorentz invariance is recovered at the end. We develop this new setting on the basis of a simple scalar model and then its applications to generalized electrodynamics and HD gravity are worked out. For a wide class of field theories this method is better suited than Ostrogradski's for a generalization to 2n-derivative theories. (author)

  16. Analysis of Green's functions and stability problem in models of quantum field theory with solitons

    International Nuclear Information System (INIS)

    Raczka, R.; Roszkowski, L.

    1983-10-01

    A class of models of quantum field theory for a multiplet phi-vector=(phi 1 ,...,phisub(N)) of real scalar fields, possessing a particle-like classical solution phi-vector 0 , is considered. A new formula for generating functional for time-ordered Green's functions in terms of effective propagators is derived. The problem of classical and quantum stability is analyzed in detail. It is shown by partly non-perturbative analysis that in the considered models the excited states of mesons do exist and form the trajectories in the plane mass 2 -spin. These trajectories are linear or approximately linear like experimental trajectories. (author)

  17. Wilson lines in quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Cherednikov, Igor Olegovich [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Mertens, Tom; Veken, Frederik F. van der [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.

    2014-07-01

    Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

  18. Wilson lines in quantum field theory

    International Nuclear Information System (INIS)

    Cherednikov, Igor Olegovich; Joint Institute of Nuclear Research, Moscow; Mertens, Tom; Veken, Frederik F. van der

    2014-01-01

    Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

  19. The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity

    Directory of Open Access Journals (Sweden)

    František FOJTÍK

    2014-06-01

    Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.

  20. Geometry of lattice field theory

    International Nuclear Information System (INIS)

    Honan, T.J.

    1986-01-01

    Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus

  1. Abelian Chern endash Simons theory. I. A topological quantum field theory

    International Nuclear Information System (INIS)

    Manoliu, M.

    1998-01-01

    We give a construction of the Abelian Chern endash Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern endash Simons theory [J. Diff. Geom. 33, 787 endash 902 (1991); Topology 32, 509 endash 529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans 68, 175 endash 186 (1989)]. copyright 1998 American Institute of Physics

  2. Introduction to classical and quantum field theory

    International Nuclear Information System (INIS)

    Ng, Tai-Kai

    2009-01-01

    This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments. Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way. Divided into three parts, the first part covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part introduces more advanced concepts and techniques. Part III discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing, 'real' physics problems. Throughout there are numerous end-of-chapter problems, and a free solutions manual is available for lecturers. (orig.)

  3. Quantum field theory with infinite component local fields as an alternative to the string theories

    Science.gov (United States)

    Krasnikov, N. V.

    1987-09-01

    We show that the introduction of the infinite component local fields with higher-order derivatives in the interaction makes the theory completely ultraviolet finite. For the γ5-anomalous theories the introduction of the infinite component field makes the theory renormalizable or even superrenormalizable. I am indebted to J. Ambjōrn, P. Di Vecchia, H.B. Nielsen and L. Rozhansky for useful discussions. It is a pleasure to thank the Niels Bohr Institute (Copenhagen) where this work was completed for kind hospitality.

  4. Workshop on Thermal Field Theory to Neural Networks

    CERN Document Server

    Veneziano, Gabriele; Aurenche, Patrick

    1996-01-01

    Tanguy Altherr was a Fellow in the Theory Division at CERN, on leave from LAPP (CNRS) Annecy. At the time of his accidental death in July 1994, he was only 31.A meeting was organized at CERN, covering the various aspects of his scientific interests: thermal field theory and its applications to hot or dense media, neural networks and its applications to high energy data analysis. Speakers were among his closest collaborators and friends.

  5. Field theory and the Standard Model

    Energy Technology Data Exchange (ETDEWEB)

    Dudas, E [Orsay, LPT (France)

    2014-07-01

    This brief introduction to Quantum Field Theory and the Standard Model contains the basic building blocks of perturbation theory in quantum field theory, an elementary introduction to gauge theories and the basic classical and quantum features of the electroweak sector of the Standard Model. Some details are given for the theoretical bias concerning the Higgs mass limits, as well as on obscure features of the Standard Model which motivate new physics constructions.

  6. Effective theories of single field inflation when heavy fields matter

    CERN Document Server

    Achucarro, Ana; Hardeman, Sjoerd; Palma, Gonzalo A; Patil, Subodh P

    2012-01-01

    We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbat...

  7. Euler-Poincare reduction for discrete field theories

    International Nuclear Information System (INIS)

    Vankerschaver, Joris

    2007-01-01

    In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

  8. Unified field theory

    International Nuclear Information System (INIS)

    Vollendorf, F.

    1976-01-01

    A theory is developed in which the gravitational as well as the electromagnetic field is described in a purely geometrical manner. In the case of a static central symmetric field Newton's law of gravitation and Schwarzschild's line element are derived by means of an action principle. The same principle leads to Fermat's law which defines the world lines of photons. (orig.) [de

  9. Virtual Learning Environments: A View from the Theory of Conceptual Fields

    Directory of Open Access Journals (Sweden)

    Iralí Araque

    2018-01-01

    Full Text Available The inclusion of communication and information technologies for formative purposes has given way to virtual learning environments, which, backed by constructivist theories, provide a theoretical and methodological framework, thus contributing to the cognitive development of students at university level, evidenced in the development of their learning schemes. The theory of conceptual fields offers an analysis of the elements of schemas and the process of knowledge construction. In this sense, the present work had as objective to raise some elements, such as teaching methodology, didactic strategies, materials and resources for learning, teacher and student roles, which should be considered in the design of virtual learning environments, in the light of the theory of conceptual fields, so as to enhance the construction of knowledge and where the emphasis of the educational process lies on learning rather than teaching. The methodology used is a documentary study, type descriptive, based on the review and bibliographical analysis of constructivist theories, as well as researchers related to the design and construction of virtual learning environments. The results show that conceptual fields theory is an excellent option to consider, as a constructivist theory, in order to consolidate the process of knowledge construction, from the individual to the collective.

  10. Consistent constraints on the Standard Model Effective Field Theory

    International Nuclear Information System (INIS)

    Berthier, Laure; Trott, Michael

    2016-01-01

    We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S,T analysis is modified by the theory errors we include as an illustrative example.

  11. Asymptotic behaviour in field theory

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, H.

    1980-07-01

    Asymptotic behaviour in field theory has been studied and the anomalies are pointed out in two specific cases, (i) the infrared and fixed angle high energy behaviour in the non-trivial case of the 'box' amplitude in a scalar-scalar theory and (ii) high energy behaviour of a sixth order Yang-Mills diagram. A set of rules are presented for writing down the precise leading infrared behaviour of an arbitrary generalised ladder diagram (GLD) in QED. These rules are the final result of a detailed analysis of the relevant amplitudes in the Feynman parameter space. The connection between the infrared and fixed angle high energy limits of generalised ladder diagrams is explained. It is argued that the same set of rules yield the fixed angle high energy limit.

  12. Austerity and geometric structure of field theories

    International Nuclear Information System (INIS)

    Kheyfets, A.

    1986-01-01

    The relation between the austerity idea and the geometric structure of the three basic field theories - electrodynamics, Yang-Mills theory, and general relativity - is studied. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity of delta dot produced with delta = 0 used twice, at the 1-2-3-dimensional level (providing the homogeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories above. This dissertation: (a) analyzes the difficulties by means of algebraic topology, integration theory, and modern differential geometry based on the concepts of principal bundles and Ehresmann connections: (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for the three theories and compatible with the original austerity idea; and (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories

  13. On background-independent open-string field theory

    International Nuclear Information System (INIS)

    Witten, E.

    1992-01-01

    A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical ''space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant open-string world-sheet theories and that, when expanding around a classical solution, the infinitesimal gauge transformations are generated by the world-sheet BRST operator

  14. An introduction to conformal field theory

    International Nuclear Information System (INIS)

    Gaberdiel, Matthias R.; Fitzwilliam College, Cambridge

    2000-01-01

    A comprehensive introduction to two-dimensional conformal field theory is given. The structure of the meromorphic subtheory is described in detail, and a number of examples are presented explicitly. Standard constructions such as the coset and the orbifold construction are explained. The concept of a representation of the meromorphic theory is introduced, and the role of Zhu's algebra in classifying highest weight representations is elucidated. The fusion product of two representations and the corresponding fusion rules are defined, and Verlinde's formula is explained. Finally, higher correlation functions are considered, and the polynomial relations of Moore and Seiberg and the quantum group structure of chiral conformal field theory are discussed. The treatment is relatively general and also allows for a description of less well known classes of theories such as logarithmic conformal field theories. (author)

  15. Metric quantum field theory: A preliminary look

    International Nuclear Information System (INIS)

    Watson, W.N.

    1988-01-01

    Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature? This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics

  16. The classical theory of fields electromagnetism

    CERN Document Server

    Helrich, Carl S

    2012-01-01

    The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dis...

  17. An introduction to effective field theory

    International Nuclear Information System (INIS)

    Donoghue, John F.

    1999-01-01

    In these lectures I describe the main ideas of effective field theory. These are first illustrated using QED and the linear sigma model as examples. Calculational techniques using both Feynman diagrams and dispersion relations are introduced. Within QCD, chiral perturbation theory is a complete effective field theory, and I give a guide to some calculations in the literature which illustrates key ideas. (author)

  18. Quantum Field Theory in (0 + 1) Dimensions

    Science.gov (United States)

    Boozer, A. D.

    2007-01-01

    We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…

  19. Cartan's equations define a topological field theory of the BF type

    International Nuclear Information System (INIS)

    Cuesta, Vladimir; Montesinos, Merced

    2007-01-01

    Cartan's first and second structure equations together with first and second Bianchi identities can be interpreted as equations of motion for the tetrad, the connection and a set of two-form fields T I and R J I . From this viewpoint, these equations define by themselves a field theory. Restricting the analysis to four-dimensional spacetimes (keeping gravity in mind), it is possible to give an action principle of the BF type from which these equations of motion are obtained. The action turns out to be equivalent to a linear combination of the Nieh-Yan, Pontrjagin, and Euler classes, and so the field theory defined by the action is topological. Once Einstein's equations are added, the resulting theory is general relativity. Therefore, the current results show that the relationship between general relativity and topological field theories of the BF type is also present in the first-order formalism for general relativity

  20. Gravitational effects in field gravitation theory

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Vlasov, A.A.

    1979-01-01

    The possibilities to describe various gravitation effects of field gravitation theory (FGT) are considered. Past-Newtonian approximation of the FGT has been constructed and on the basis of this approximation it has been shown that the field theory allows one to describe the whole set of experimental facts. The comparison of post-Newtonian parameters in FGT with those in the Einstein's theory makes it clear that these two; theories are undistinguishable from the viewpoint of any experiments, realized with post-Newtonian accuracy. Gravitational field of an island type source with spherically symmetrical distribution of matter and unstationary homogeneous model of Universe, which allows to describe the effect of cosmological red shift, are considered

  1. Knots, topology and quantum field theories

    International Nuclear Information System (INIS)

    Lusanna, L.

    1989-01-01

    The title of the workshop, Knots, Topology and Quantum Field Theory, accurate reflected the topics discussed. There have been important developments in mathematical and quantum field theory in the past few years, which had a large impact on physicist thinking. It is historically unusual and pleasing that these developments are taking place as a result of an intense interaction between mathematical physicists and mathematician. On the one hand, topological concepts and methods are playing an increasingly important lead to novel mathematical concepts: for instance, the study of quantum groups open a new chapter in the deformation theory of Lie algebras. These developments at present will lead to new insights into the theory of elementary particles and their interactions. In essence, the talks dealt with three, broadly defined areas of theoretical physics. One was topological quantum field theories, the other the problem of quantum groups and the third one certain aspects of more traditional field theories, such as, for instance, quantum gravity. These topics, however, are interrelated and the general theme of the workshop defies rigid classification; this was evident from the cross references to be found in almo all the talks

  2. An introduction to conformal field theory in two dimensions and string theory

    International Nuclear Information System (INIS)

    Wadia, S.R.

    1989-01-01

    This paper provides information on The S-Matrix; Elements of conformally invariant field theory in 2-dim.; The Virasoro gauge conditions; Some representations of the Virasoro algebra; The S-matrix of the Bosonic string theory; Super conformal field theory; Superstring; superstring spectrum and GSO projection; The (β,γ) ghost system; BRST formulation; and String propagation in background fields

  3. Path integral quantization of parametrized field theory

    International Nuclear Information System (INIS)

    Varadarajan, Madhavan

    2004-01-01

    Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrized field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary, in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrized field theory in order to analyze issues at the interface of quantum field theory and general covariance in a path integral context. We show that the measure in the Lorentzian path integral is nontrivial and is the analog of the Fradkin-Vilkovisky measure for quantum gravity. We construct Euclidean functional integrals in the generally covariant setting of parametrized field theory using key ideas of Schleich and show that our constructions imply the existence of nonstandard 'Wick rotations' of the standard free scalar field two-point function. We develop a framework to study the problem of time through computations of scalar field two-point functions. We illustrate our ideas through explicit computation for a time independent (1+1)-dimensional foliation. Although the problem of time seems to be absent in this simple example, the general case is still open. We discuss our results in the contexts of the path integral formulation of quantum gravity and the canonical quantization of parametrized field theory

  4. Nonlocal quantum field theory

    International Nuclear Information System (INIS)

    Efimov, G.V.

    1976-01-01

    The basic ideas for creating the theory of nonlocal interactions of a scalar one-component field are presented. Lagrangian describing a non-interacting field is the ordinary one so that non-interacting particles are described by standard methods of the Fock space. Form factors introduced have been chosen from a class of analytic functionals and quantized. Conditions of microcausality have been considered in detail. The convergence of all integrals corresponding to the arbitrary Feynman diagrams in spinor electrodynamics is guaranteed in the frame of the rules formulated. It is noted in conclusion that the spinor electrodynamics with nonlocal interaction contains no ultraviolet divergencies and satisfies all the requirements of the quantum field theory; in this sense it is mathematically more consistent than its local version

  5. On Noethers theorem in quantum field theory

    International Nuclear Information System (INIS)

    Buchholz, D.; Doplicher, S.; Longo, R.

    1985-03-01

    Extending an earlier construction of local generators of symmetries in (S. Doplicher, 1982) to space-time and supersymmetries, we establish a weak form of Noethers theorem in quantum field theory. We also comment on the physical significance of the 'split property', underlying our analysis, and discuss some local aspects of superselection rules following from our results. (orig./HSI)

  6. Two-dimensional topological field theories coupled to four-dimensional BF theory

    International Nuclear Information System (INIS)

    Montesinos, Merced; Perez, Alejandro

    2008-01-01

    Four-dimensional BF theory admits a natural coupling to extended sources supported on two-dimensional surfaces or string world sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two-dimensional world sheet. We show how two-dimensional Yang-Mills degrees of freedom can be added on the world sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two-dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background-independent quantum field theory where local degrees of freedom at low energies arise from global topological (world sheet) degrees of freedom at the fundamental level

  7. OPE convergence in non-relativistic conformal field theories

    Energy Technology Data Exchange (ETDEWEB)

    Goldberger, Walter D.; Khandker, Zuhair University; Prabhu, Siddharth [Department of Physics, Yale University,New Haven, CT 06511 (United States); Physics Department, Boston University,Boston, MA 02215 (United States)

    2015-12-09

    Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NRCFT, in particular the mapping between operators and states in a non-relativistic “radial quantization” Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a demonstration of convergence of the (imaginary time) OPE in certain kinematic limits, and an estimate of the decay rate of the OPE tail inside matrix elements which, as in relativistic CFTs, depends exponentially on operator dimensions. To illustrate our results we consider several examples, including a strongly interacting field theory of bosons tuned to the unitarity limit, as well as a class of holographic models. Given the similarity with known statements about the OPE in SO(2,d) invariant field theories, our results suggest the existence of a bootstrap approach to constraining NRCFTs, with applications to bound state spectra and interactions. We briefly comment on a possible implementation of this non-relativistic conformal bootstrap program.

  8. Fundamental problems of gauge field theory

    International Nuclear Information System (INIS)

    Velo, G.; Wightman, A.S.

    1986-01-01

    As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now provides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lecture notes collected in this volume concentrate on the many unsolved problems which arise here, and on the general ideas and methods which have been proposed for their solution. In particular, the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the exploration of the extraordinary enigmatic connections between Kac-Moody-Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories are mentioned

  9. A novel string field theory solving string theory by liberating left and right movers

    International Nuclear Information System (INIS)

    Nielsen, Holger B.; Ninomiya, Masao

    2014-01-01

    We put forward ideas to a novel string field theory based on making some “objects” that essentially describe “liberated” left- and right- mover fields X L μ (τ+σ) and X R μ (τ−σ) on the string. Our novel string field theory is completely definitely different from any other string theory in as far as a “null set” of information in the string field theory Fock space has been removed relatively, to the usual string field theories. So our theory is definitely new. The main progress is that we manage to make our novel string field theory provide the correct mass square spectrum for the string. We finally suggest how to obtain the Veneziano amplitude in our model

  10. Hidden gravity in open-string field theory

    International Nuclear Information System (INIS)

    Siegel, W.

    1994-01-01

    We clarify the nature of the graviton as a bound state in open-string field theory: The flat metric in the action appears as the vacuum value of an open string field. The bound state appears as a composite field in the free field theory

  11. Field theory of relativistic strings: I. Trees

    International Nuclear Information System (INIS)

    Kaku, M.; Kikkawa, K.

    1985-01-01

    The authors present an entirely new kind of field theory, a field theory quantized not at space-time points, but quantized along an extended set of multilocal points on a string. This represents a significant departure from the usual quantum field theory, whose free theory represents a definite set of elementary particles, because the field theory on relativistic strings can accommodate an infinite set of linearly rising Regge trajectories. In this paper, the authors (1) present canonical quantization and the Green's function of the free string, (2) introduce three-string interactions, (3) resolve the question of multiple counting, (4) complete the counting arguments for all N-point trees, and (5) introduce four-string interactions which yield a Yang-Mills structure when the zero-slope limit is taken

  12. Conformal field theories and tensor categories. Proceedings

    Energy Technology Data Exchange (ETDEWEB)

    Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics

    2014-08-01

    First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

  13. Conformal field theories and tensor categories. Proceedings

    International Nuclear Information System (INIS)

    Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph

    2014-01-01

    First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

  14. Neural fields theory and applications

    CERN Document Server

    Graben, Peter; Potthast, Roland; Wright, James

    2014-01-01

    With this book, the editors present the first comprehensive collection in neural field studies, authored by leading scientists in the field - among them are two of the founding-fathers of neural field theory. Up to now, research results in the field have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. Starting with a tutorial for novices in neural field studies, the book comprises chapters on emergent patterns, their phase transitions and evolution, on stochastic approaches, cortical development, cognition, robotics and computation, large-scale numerical simulations, the coupling of neural fields to the electroencephalogram and phase transitions in anesthesia. The intended readership are students and scientists in applied mathematics, theoretical physics, theoretical biology, and computational neuroscience. Neural field theory and its applications have a long-standing tradition in the mathematical and computational ...

  15. Twistor-theoretic approach to topological field theories

    International Nuclear Information System (INIS)

    Ito, Kei.

    1991-12-01

    The two-dimensional topological field theory which describes a four-dimensional self-dual space-time (gravitational instanton) as a target space, which we constructed before, is shown to be deeply connected with Penrose's 'twistor theory'. The relations are presented in detail. Thus our theory offers a 'twistor theoretic' approach to topological field theories. (author)

  16. The S-matrix of superstring field theory

    International Nuclear Information System (INIS)

    Konopka, Sebastian

    2015-01-01

    We show that the classical S-matrix calculated from the recently proposed superstring field theories give the correct perturbative S-matrix. In the proof we exploit the fact that the vertices are obtained by a field redefinition in the large Hilbert space. The result extends to include the NS-NS subsector of type II superstring field theory and the recently found equations of motions for the Ramond fields. In addition, our proof implies that the S-matrix obtained from Berkovits’ WZW-like string field theory then agrees with the perturbative S-matrix to all orders.

  17. A non-linear field theory

    International Nuclear Information System (INIS)

    Skyrme, T.H.R.

    1994-01-01

    A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs

  18. Statistical mechanics and field theory

    International Nuclear Information System (INIS)

    Samuel, S.A.

    1979-05-01

    Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks. 64 references

  19. Effective field theory analysis of Higgs naturalness

    Energy Technology Data Exchange (ETDEWEB)

    Bar-Shalom, Shaouly [Technion-Israel Inst. of Tech., Haifa (Israel); Soni, Amarjit [Brookhaven National Lab. (BNL), Upton, NY (United States); Wudka, Jose [Univ. of California, Riverside, CA (United States)

    2015-07-20

    Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.

  20. Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories

    International Nuclear Information System (INIS)

    Sasai, Yuya; Sasakura, Naoki

    2008-01-01

    Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar φ 4 braided noncommutative field theory in Lie-algebraic noncommutative space-time, [x i ,x j ]=2iκε ijk x k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter κ. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry

  1. Effective field theory analysis of double Higgs production via gluon fusion

    CERN Document Server

    Azatov, Aleksandr; Panico, Giuliano; Son, Minho

    2015-01-01

    We perform a detailed study of double Higgs production via gluon fusion in the Effective Field Theory (EFT) framework where effects from new physics are parametrized by local operators. Our analysis provides a perspective broader than the one followed in most of the previous analyses, where this process was merely considered as a way to extract the Higgs trilinear coupling. We focus on the $hh \\to b\\bar b\\gamma\\gamma$ channel and perform a thorough simulation of signal and background at the 14 TeV LHC and a future 100 TeV proton-proton collider. We make use of invariant mass distributions to enhance the sensitivity on the EFT coefficients and give a first assessment of the impact of jet substructure techniques on the results. The range of validity of the EFT description is estimated, as required to consistently exploit the high-energy range of distributions, pointing out the potential relevance of dimension-8 operators. Our analysis contains a few important improvements over previous studies and identifies so...

  2. Conformal field theories and critical phenomena

    International Nuclear Information System (INIS)

    Xu, Bowei

    1993-01-01

    In this article we present a brief review of the conformal symmetry and the two dimensional conformal quantum field theories. As concrete applications of the conformal theories to the critical phenomena in statistical systems, we calculate the value of central charge and the anomalous scale dimensions of the Z 2 symmetric quantum chain with boundary condition. The results are compatible with the prediction of the conformal field theories

  3. Local algebras in Euclidean quantum field theory

    International Nuclear Information System (INIS)

    Guerra, Francesco.

    1975-06-01

    The general structure of the local observable algebras of Euclidean quantum field theory is described, considering the very simple examples of the free scalar field, the vector meson field, and the electromagnetic field. The role of Markov properties, and the relations between Euclidean theory and Hamiltonian theory in Minkowski space-time are especially emphasized. No conflict appears between covariance (in the Euclidean sense) and locality (in the Markov sense) on one hand and positive definiteness of the metric on the other hand [fr

  4. UV / IR mixing in noncommutative field theory via open string loops

    International Nuclear Information System (INIS)

    Kiem, Youngjai; Lee, Sangmin

    2000-01-01

    We explicitly evaluate one-loop (annulus) planar and nonplanar open string amplitudes in the presence of the background NS-NS two-form field. In the decoupling limit of Seiberg and Witten, we find that the nonplanar string amplitudes reproduce the UV/IR mixing of noncommutative field theories. In particular, the investigation of the UV regime of the open string amplitudes shows that certain IR closed string degrees of freedom survive the decoupling limit as previously predicted from the noncommutative field theory analysis. These degrees of freedom are responsible for the quadratic, linear and logarithmic IR singularities when the D-branes embedded in space-time have the codimension zero, one and two, respectively. The analysis is given for both bosonic and supersymmetric open strings

  5. Using field theory in hadron physics

    International Nuclear Information System (INIS)

    Abarbanel, H.D.I.

    1978-03-01

    Topics are covered on the connection of field theory and hadron physics. The renormalization group and infrared and ultraviolet limits of field theory, in particular quantum chromodynamics, spontaneous mass generation, color confinement, instantons, and the vacuum state in quantum chromodynamics are treated. 21 references

  6. Finite-temperature field theory

    International Nuclear Information System (INIS)

    Kapusta, J.I.; Landshoff, P.V.

    1989-01-01

    Particle number is not conserved in relativistic theories although both lepton and baryon number are. Therefore when discussing the thermodynamics of a quantum field theory one uses the grand canonical formalism. The entropy S is maximised, keeping fixed the ensemble averages E and N of energy and lepton number. Two lagrange multipliers are introduced. (author)

  7. Effective field theory for NN interactions

    International Nuclear Information System (INIS)

    Tran Duy Khuong; Vo Hanh Phuc

    2003-01-01

    The effective field theory of NN interactions is formulated and the power counting appropriate to this case is reviewed. It is more subtle than in most effective field theories since in the limit that the S-wave NN scattering lengths go to infinity. It is governed by nontrivial fixed point. The leading two body terms in the effective field theory for nucleon self interactions are scale invariant and invariant under Wigner SU(4) spin-isospin symmetry in this limit. Higher body terms with no derivatives (i.e. three and four body terms) are automatically invariant under Wigner symmetry. (author)

  8. Four-dimensional boson field theory. II. Existence

    International Nuclear Information System (INIS)

    Baker, G.A. Jr.

    1986-01-01

    The existence of the continuum, quantum field theory found by Baker and Johnson [G. A. Baker, Jr. and J. D. Johnson, J. Phys. A 18, L261 (1985)] to be nontrivial is proved rigorously. It is proved to satisfy all usual requirements of such a field theory, except rotational invariance. Currently known information is consistent with rotational invariance however. Most of the usual properties of other known Euclidean boson quantum field theories hold here, in a somewhat weakened form. Summability of the sufficiently strongly ultraviolet cutoff bare coupling constant perturbation series is proved as well as a nonzero radius of convergence for high-temperature expansions of the corresponding continuous-spin Ising model. The description of the theory by these two series methods is shown to be equivalent. The field theory is probably not asymptotically free

  9. Statistical mechanics and stability of random lattice field theory

    International Nuclear Information System (INIS)

    Baskaran, G.

    1984-01-01

    The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities. (orig.)

  10. Moduli spaces of unitary conformal field theories

    International Nuclear Information System (INIS)

    Wendland, K.

    2000-08-01

    We investigate various features of moduli spaces of unitary conformal field theories. A geometric characterization of rational toroidal conformal field theories in arbitrary dimensions is presented and discussed in relation to singular tori and those with complex multiplication. We study the moduli space M 2 of unitary two-dimensional conformal field theories with central charge c = 2. All the 26 non-exceptional non-isolated irreducible components of M 2 are constructed that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly. All multicritical points and lines are determined, such that all but three of these 26 components are directly or indirectly connected to the space of toroidal theories in M 2 . Relating our results to those by Dixon, Ginsparg, Harvey on the classification of c = 3/2 superconformal field theories, we give geometric interpretations to all non-isolated orbifolds discussed by them and correct their statements on multicritical points within the moduli space of c = 3/2 superconformal field theories. In the main part of this work, we investigate the moduli space M of N = (4, 4) superconformal field theories with central charge c = 6. After a slight emendation of its global description we give generic partition functions for models contained in M. We explicitly determine the locations of various known models in the component of M associated to K3 surfaces

  11. Three-dimensional N=6 superconformal field theories and their membrane dynamics

    International Nuclear Information System (INIS)

    Berenstein, David; Trancanelli, Diego

    2008-01-01

    We analyze several aspects of the recent construction of three-dimensional conformal gauge theories by Aharony et al. in various regimes. We pay special attention to understanding how the M-theory geometry and interpretation can be extracted from the analysis of the field theory. We revisit the calculations of the moduli space of vacua and the complete characterization of chiral ring operators by analyzing the field theory compactified on a 2-sphere. We show that many of the states dual to these operators can be interpreted as D-brane states in the weak-coupling limit. Also, various features of the dual AdS geometry can be obtained by performing a strong coupling expansion around moduli space configurations, even though one is not taking the planar expansion. In particular, we show that at strong coupling the corresponding weak-coupling D-brane states of the chiral ring localize on particular submanifolds of the dual geometry that match the M-theory interpretation. We also study the massive spectrum of fields in the moduli space. We use this to investigate the dispersion relation of giant magnons from the field theory point of view. Our analysis predicts the exact functional form of the dispersion relation as a function of the world sheet momentum, independently of integrability assumptions, but not the exact form with respect to the 't Hooft coupling. We also get the dispersion relation of bound states of giant magnons from first principles, providing evidence for the full integrability of the corresponding spin chain model at strong 't Hooft coupling.

  12. Effective quantum field theories

    International Nuclear Information System (INIS)

    Georgi, H.M.

    1989-01-01

    Certain dimensional parameters play a crucial role in the understanding of weak and strong interactions based on SU(2) x U(1) and SU(3) symmetry group theories and of grand unified theories (GUT's) based on SU(5). These parameters are the confinement scale of quantum chromodynamics and the breaking scales of SU(2) x U(1) and SU(5). The concepts of effective quantum field theories and renormalisability are discussed with reference to the economics and ethics of research. (U.K.)

  13. Quantum Field Theory in a Semiotic Perspective

    CERN Document Server

    Günter Dosch, Hans; Sieroka, Norman

    2005-01-01

    Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly ac...

  14. Scattering and short-distance properties in field theory models

    International Nuclear Information System (INIS)

    Iagolnitzer, D.

    1987-01-01

    The aim of constructive field theory is not only to define models but also to establish their general properties of physical interest. We here review recent works on scattering and on short-distance properties for weakly coupled theories with mass gap such as typically P(φ) in dimension 2, φ 4 in dimension 3 and the (renormalizable, asymptotically free) massive Gross-Neveu (GN) model in dimension 2. Many of the ideas would apply similarly to other (possibly non renormalizable) theories that might be defined in a similar way via phase-space analysis

  15. Quantum field theory for the gifted amateur

    CERN Document Server

    Lancaster, Tom

    2014-01-01

    Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in ...

  16. New results in topological field theory and Abelian gauge theory

    International Nuclear Information System (INIS)

    Thompson, G.

    1995-10-01

    These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs

  17. New results in topological field theory and Abelian gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Thompson, G

    1995-10-01

    These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs.

  18. Statistical predictions from anarchic field theory landscapes

    International Nuclear Information System (INIS)

    Balasubramanian, Vijay; Boer, Jan de; Naqvi, Asad

    2010-01-01

    Consistent coupling of effective field theories with a quantum theory of gravity appears to require bounds on the rank of the gauge group and the amount of matter. We consider landscapes of field theories subject to such to boundedness constraints. We argue that appropriately 'coarse-grained' aspects of the randomly chosen field theory in such landscapes, such as the fraction of gauge groups with ranks in a given range, can be statistically predictable. To illustrate our point we show how the uniform measures on simple classes of N=1 quiver gauge theories localize in the vicinity of theories with certain typical structures. Generically, this approach would predict a high energy theory with very many gauge factors, with the high rank factors largely decoupled from the low rank factors if we require asymptotic freedom for the latter.

  19. Vacuum instability in scalar field theories

    International Nuclear Information System (INIS)

    McKane, A.J.

    1978-09-01

    Scalar field theories with an interaction of the form gphisup(N) have no stable vacuum state for some range of values of their coupling constant, g. This thesis reports calculations of vacuum instability in such theories. Using the idea that the tunnelling out of the vacuum state is described by the instanton solutions of the theory, the imaginary part of the vertex functions is calculated for the massless theory in the one-loop approximation, near the dimension dsub(c) = 2N/N-2, where the theory is just renormalisable. The calculation differs from previous treatments in that dimensional regularisation is used to control the ultra-violet divergences of the theory. In this way previous analytic calculations in conformally invariant field theories are extended to the case where the theory is almost conformally invariant, since it is now defined in dsub(c) - epsilon dimensions (epsilon > 0). (author)

  20. Thermo field dynamics: a quantum field theory at finite temperature

    International Nuclear Information System (INIS)

    Mancini, F.; Marinaro, M.; Matsumoto, H.

    1988-01-01

    A brief review of the theory of thermo field dynamics (TFD) is presented. TFD is introduced and developed by Umezawa and his coworkers at finite temperature. The most significant concept in TFD is that of a thermal vacuum which satisfies some conditions denoted as thermal state conditions. The TFD permits to reformulate theories at finite temperature. There is no need in an additional principle to determine particle distributions at T ≠ 0. Temperature and other macroscopic parameters are introduced in the definition of the vacuum state. All operator formalisms used in quantum field theory at T=0 are preserved, although the field degrees of freedom are doubled. 8 refs

  1. Quantum field theory in a semiotic perspective

    International Nuclear Information System (INIS)

    Dosch, H.G.

    2005-01-01

    Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincare, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)

  2. Quantum field theory in a semiotic perspective

    Energy Technology Data Exchange (ETDEWEB)

    Dosch, H.G. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Mueller, V.F. [Technische Univ. Kaiserslautern (Germany). Fachbereich Physik; Sieroka, N. [Zurich Univ. (Switzerland)

    2005-07-01

    Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincare, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)

  3. Semiclassical analysis of the weak-coupling limit of SU(2) lattice gauge theory: The subspace of constant fields

    International Nuclear Information System (INIS)

    Bartels, J.; Wu, T.T.

    1988-01-01

    This paper contains the first part of a systematic semiclassical analysis of the weak-coupling limit of lattice gauge theories, using the Hamiltonian formulation. The model consists of an N 3 cubic lattice of pure SU(2) Yang-Mills theory, and in this first part we limit ourselves to the subspace of constant field configurations. We investigate the flow of classical trajectories, with a particular emphasis on the existence and location of caustics. There the ground-state wave function is expected to peak. It is found that regions densely filled with caustics are very close to the origin, i.e., in the domain of weak field configurations. This strongly supports the expectation that caustics are essential for quantities of physical interest

  4. Quantum field theory on brane backgrounds

    International Nuclear Information System (INIS)

    Flachi, A.

    2001-11-01

    The development of higher dimensional quantum field theories is reviewed from the older Kaluza-Klein theory to the new brane models, emphasising their relevance in modern particle physics. The issue of spontaneous symmetry breaking in the Randall-Sundrum model is considered. The role of the coupling between bulk fields and the curvature is investigated and a model in favour of bulk symmetry breaking is presented. The lowest order quantum corrections arising from a quantized scalar field in the Randall-Sundrum spacetime are computed. A careful discussion of the boundary conditions as well as the renormalization is provided. The massless case is also discussed and a proof of the vanishing of the conformal anomaly in this model is given. An analysis of the self-consistency is presented and the radius stabilization problem studied. It is shown that quantum effects may provide a stabilization of the radius, nevertheless, when the hierarchy problem is simultaneously solved, fine tuning of the brane tensions is necessary. The previous results are extended in order to include the contribution to the one-loop effective action from fermions. The boundary conditions are discussed and their relation with gauge invariance accurately examined. The possibility of breaking the gauge symmetries by using Wilson-loops is investigated. The analysis of the self- consistency is extended when the contribution of fermions is included, and it is shown that also in this case it is not possible to stabilize the radius and simultaneously solving the hierarchy problem, unless the brane tensions are fine tuned to a high degree. (author)

  5. Field theories with multiple fermionic excitations

    International Nuclear Information System (INIS)

    Crawford, J.P.

    1978-01-01

    The reason for the existence of the muon has been an enigma since its discovery. Since that time there has been a continuing proliferation of elementary particles. It is proposed that this proliferation of leptons and quarks is comprehensible if there are only four fundamental particles, the leptons ν/sub e/ and e - , and the quarks u and d. All other leptons and quarks are imagined to be excited states of these four fundamental entities. Attention is restricted to the charged leptons and the electromagnetic interactions only. A detailed study of a field theory in which there is only one fundamental charged fermionic field having two (or more) excitations is made. When the electromagnetic interactions are introduced and the theory is second quantized, under certain conditions this theory reproduces the S matrix obtained from usual OED. In this case no electromagnetic transitions are allowed. A leptonic charge operator is defined and a superselection rule for this leptonic charge is found. Unfortunately, the mass spectrum cannot be obtained. This theory has many renormalizable generalizations including non-abelian gauge theories, Yukawa-type theories, and Fermi-type theories. Under certain circumstances the Yukawa- and Fermi-type theories are finite in perturbation theory. It is concluded that there are no fundamental objections to having fermionic fields with more than one excitation

  6. Light-front quantization of field theory

    Energy Technology Data Exchange (ETDEWEB)

    Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

    1996-07-01

    Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs.

  7. Light-front quantization of field theory

    International Nuclear Information System (INIS)

    Srivastava, Prem P.

    1996-07-01

    Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs

  8. Quantum field theory of point particles and strings

    CERN Document Server

    Hatfield, Brian

    1992-01-01

    The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string.

  9. Flat holography: aspects of the dual field theory

    Energy Technology Data Exchange (ETDEWEB)

    Bagchi, Arjun [Indian Institute of Technology Kanpur,Kalyanpur, Kanpur 208016 (India); Center for Theoretical Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Basu, Rudranil [Saha Institute of Nuclear Physics,Block AF, Sector 1, Bidhannagar, Kolkata 700068 (India); Kakkar, Ashish [Indian Institute of Science Education and Research,Dr Homi Bhabha Road, Pashan, Pune 411008 (India); Mehra, Aditya [Indian Institute of Technology Kanpur,Kalyanpur, Kanpur 208016 (India); Indian Institute of Science Education and Research,Dr Homi Bhabha Road, Pashan, Pune 411008 (India)

    2016-12-29

    Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk – 2d boundary case and then focus on the 4d bulk – 3d boundary example, where the symmetry in question is the infinite dimensional BMS{sub 4} algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D=4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.

  10. Correlated effective field theory in transition metal compounds

    International Nuclear Information System (INIS)

    Mukhopadhyay, Subhasis; Chatterjee, Ibha

    2004-01-01

    Mean field theory is good enough to study the physical properties at higher temperatures and in higher dimensions. It explains the critical phenomena in a restricted sense. Near the critical temperatures, when fluctuations become important, it may not give the correct results. Similarly in low dimensions, the correlations become important and the mean field theory seems to be inadequate to explain the physical phenomena. At low-temperatures too, the quantum correlations become important and these effects are to be treated in an appropriate way. In 1974, Prof. M.E. Lines of Bell Laboratories, developed a theory which goes beyond the mean field theory and is known as the correlated effective field (CEF) theory. It takes into account the fluctuations in a semiempirical way. Lines and his collaborators used this theory to explain the short-range correlations and their anisotropy in the paramagnetic phase. Later Suzuki et al., Chatterjee and Desai, Mukhopadhyay and Chatterjee applied this theory to the magnetically ordered phase and a tremendous success of the theory has been found in real systems. The success of the CEF theory is discussed in this review. In order to highlight the success of this theory, earlier effective field theories and their improvements over mean field theories e.g., Bethe-Peierls-Weiss method, reaction field approximation, etc., are also discussed in this review for completeness. The beauty of the CEF theory is that it is mean field-like, but captures the essential physics of real systems to a great extent. However, this is a weak correlated theory and as a result is inappropriate for the metallic phase when strong correlations become important. In recent times, transition metal oxides become important due to the discovery of the high-temperature superconductivity and the colossal magnetoresistance phenomena. These oxides seem to be Mott insulators and undergo an insulator to metal transition by applying magnetic field, pressure and by changing

  11. Pilot-wave approaches to quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Struyve, Ward, E-mail: Ward.Struyve@fys.kuleuven.be [Institute of Theoretical Physics, K.U.Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Institute of Philosophy, K.U.Leuven, Kardinaal Mercierplein 2, B-3000 Leuven (Belgium)

    2011-07-08

    The purpose of this paper is to present an overview of recent work on pilot-wave approaches to quantum field theory. In such approaches, systems are not only described by their wave function, as in standard quantum theory, but also by some additional variables. In the non-relativistic pilot-wave theory of deBroglie and Bohm those variables are particle positions. In the context of quantum field theory, there are two natural choices, namely particle positions and fields. The incorporation of those variables makes it possible to provide an objective description of nature in which rather ambiguous notions such as 'measurement' and 'observer' play no fundamental role. As such, the theory is free of the conceptual difficulties, such as the measurement problem, that plague standard quantum theory.

  12. Dual field theories of quantum computation

    International Nuclear Information System (INIS)

    Vanchurin, Vitaly

    2016-01-01

    Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N+1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N

  13. Superconformal partial waves in Grassmannian field theories

    Energy Technology Data Exchange (ETDEWEB)

    Doobary, Reza; Heslop, Paul [Department of Mathematical Sciences, Durham University,South Road, Durham, DH1 3LE United Kingdom (United Kingdom)

    2015-12-23

    We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr(m|n,2m|2n) for all m,n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4 SYM (m=n=2) and in N=2 superconformal field theories in four dimensions (m=2,n=1) on analytic superspace. It also includes four-point functions of all (arbitrary dimension) scalar fields in non-supersymmetric conformal field theories (m=2,n=0) on Minkowski space, as well as those of a certain class of representations of the compact SU(2n) coset spaces. As an application we then specialise to N=4 SYM and use these results to perform a detailed superconformal partial wave analysis of the four-point functions of arbitrary weight half BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the 〈2222〉, 〈2233〉 and 〈3333〉 cases in an SU(N) gauge theory at finite N. The 〈2233〉 correlator predicts a non-trivial protected twist four sector for 〈3333〉 which we can completely determine using the knowledge that there is precisely one such protected twist four operator for each spin.

  14. Fractional Quantum Field Theory: From Lattice to Continuum

    Directory of Open Access Journals (Sweden)

    Vasily E. Tarasov

    2014-01-01

    Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.

  15. Quantum-field theories as representations of a single $^\\ast$-algebra

    OpenAIRE

    Raab, Andreas

    2013-01-01

    We show that many well-known quantum field theories emerge as representations of a single $^\\ast$-algebra. These include free quantum field theories in flat and curved space-times, lattice quantum field theories, Wightman quantum field theories, and string theories. We prove that such theories can be approximated on lattices, and we give a rigorous definition of the continuum limit of lattice quantum field theories.

  16. Calculations in perturbative string field theory

    International Nuclear Information System (INIS)

    Thorn, C.B.

    1987-01-01

    The author discusses methods for evaluating the Feynman diagrams of string field theory, with particular emphasis on Witten's version of open string field theory. It is explained in some detail how the rules states by Giddings and Martinec for relating a given diagram to a Polyakov path integral emerge from the Feynman rules

  17. Introduction to conformal field theory and string theory

    International Nuclear Information System (INIS)

    Dixon, L.J.

    1989-12-01

    These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs

  18. A simple proof of orientability in colored group field theory.

    Science.gov (United States)

    Caravelli, Francesco

    2012-01-01

    Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead a field at the boundary between graph theory and combinatorial topology and deals with n-simplices as colored graphs. Several techniques have been introduced in order to study the topology of the pseudo-manifold associated to the colored graph. Although of the similarity between colored group field theory and the theory of crystallizations, the connection between the two fields has never been made explicit. In this short note we use results from the theory of crystallizations to prove that color in group field theories guarantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. Colored group field theories generate orientable pseudo-manifolds. The origin of orientability is the presence of two interaction vertices in the action of colored group field theories. In order to obtain the result, we made the connection between the theory of crystallizations and colored group field theory.

  19. Quantum field theory in a nutshell

    CERN Document Server

    Zee, A

    2010-01-01

    Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading

  20. A Yang-Mills structure for string field theory

    International Nuclear Information System (INIS)

    Tsousheung Tsun

    1990-01-01

    String theorists believe that one way to achieve a fully quantized theory of string is through string field theory. The other way is to study conformal field theory on Riemann surfaces of different genera, which is the subject of many of the talks at this Conference. In a way, string field theory is the more conservative approach, since it aims just to replace the spacetime points of conventional quantum field theory by string, which are extended objects. However, from this point of view string theory has one rather unsatisfactory aspect, in the sense that although it has been very well developed and minutely studied, we are still rather unclear about its basic structure. We can contrast this to both general relativity, which is based on the geometry of spacetime, and to gauge theory, which is about the structure of various natural bundles over spacetime. And yet string theory is supposed to embody both these two essentially geometric theories. To paraphrase Witten, in string theory we seem to have to work backwards to get at the still unknown basic structure. Some joint work with Chan Hong-Mo is reported in an attempt to gain some understanding in that general direction. It seems that one could in some sense consider string field theory as a generalized Yang-Mills theory. This idea is explored. (author)

  1. Gauged BRST symmetry and the occurence of higher cocycles in quantum field theory

    International Nuclear Information System (INIS)

    Baulieu, L.; Grossman, B.; Stora, R.

    1986-06-01

    The BRST symmetry of Yang Mills theories can be gauged via the introduction of an anticommuting single gauge field. There follows the construction of a local BRST operation which allows an algebraic analysis of the BRST current algebra. This construction provides, in particular, a field theory interpretation of most higher cocycles which accompany the usual chiral anomaly

  2. Building Theory from Data in the Field of Entrepreneurship

    DEFF Research Database (Denmark)

    Mäkelä, Markus; Turcan, Romeo V.

    In this paper, we describe the process of building of grounded theory. We have an emphasis on the field of entrepreneurship: we describe and analyse current grounded theory research in entrepreneurship and point out directions and potential improvements for future research. A basis for our...... assessment of the current state of grounded theory research in entrepreneurship and for our suggestions for the future is provided by an analysis that we have conducted of recent grounded theory-based entrepreneurship research that has been published in top-tier research journals. Our paper has two goals....... First, we wish to provide an explicit paradigmatic positioning of the grounded theory methodology, discussing the most relevant views of ontologies and epistemologies that can be used as alternative starting points on conducting grounded theory research. Currently, different paradigms are used...

  3. Growing up with field theory

    International Nuclear Information System (INIS)

    Vajskopf, V.F.

    1982-01-01

    The article deals with the history of the development of quantum electrodynamics since the date of publishing the work by P.A.M. Dirac ''The Quantum Theory of the Emission and Absorption of Radiation''. Classic ''before-Dirac'' electrodynamics related with the names of Maxwell, Lorenz, Hertz, is outlined. Work of Bohr and Rosenfeld is shown to clarify the physical sense of quantized field and to reveal the existence of uncertainties between the strengths of different fields. The article points to the significance of the article ''Quantum theory of radiation'' by E. Fermi which clearly describes the Dirac theory of radiation, relativistic wave equation and fundamentals of quantum electrodynamics. Shown is work on elimination of troubles related with the existence of states with negative kinetic energy or with negative mass. Hypothesis on the Dirac filled-in vacuum led to understanding of the existence of antiparticles and two unknown till then fundamental processes - pair production and annihilation. Ways of fighting against the infinite quantities in quantum electrodynamics are considered. Renormalization of the theory overcame all the infinities and gave a pattern for calculation of any processes of electron interactions with electromagnetic field to any desired accuracy

  4. Two problems in thermal field theory

    Indian Academy of Sciences (India)

    In this talk, I review recent progress made in two areas of thermal field theory. In par- ticular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate. Keywords. Thermal field theory; quark-gluon plasma. PACS Nos 11.10.Wx; 12.38.

  5. Magnetic fields, special relativity and potential theory elementary electromagnetic theory

    CERN Document Server

    Chirgwin, B H; Kilmister, C W

    1972-01-01

    Magnetic Fields, Special Relativity and Potential Theory is an introduction to electromagnetism, special relativity, and potential theory, with emphasis on the magnetic field of steady currents (magnetostatics). Topics covered range from the origin of the magnetic field and the magnetostatic scalar potential to magnetization, electromagnetic induction and magnetic energy, and the displacement current and Maxwell's equations. This volume is comprised of five chapters and begins with an overview of magnetostatics, followed by a chapter on the methods of solving potential problems drawn from elec

  6. The space-time operator product expansion in string theory duals of field theories

    International Nuclear Information System (INIS)

    Aharony, Ofer; Komargodski, Zohar

    2008-01-01

    We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting ('single-trace') terms in the OPE of the field theory arise in this limit from the OPE of the worldsheet theory of the string dual, using a dominant saddle point which appears in computations of worldsheet correlation functions in the space-time OPE limit. The worldsheet OPE generically contains only non-physical operators, but all the non-physical contributions are resummed by the saddle point to a contribution similar to that of a physical operator, which exactly matches the field theory expectations. We verify that the OPE limit of the worldsheet theory does not have any other contributions to the OPE limit of space-time correlation functions. Our discussion is completely general and applies to any local field theory (conformal at high energies) that has a weakly coupled string theory dual (with arbitrary curvature). As a first application, we compare our results to a proposal of R. Gopakumar for the string theory dual of free gauge theories

  7. Matrix model approximations of fuzzy scalar field theories and their phase diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)

    2015-12-29

    We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.

  8. Topological quantum field theory and four manifolds

    CERN Document Server

    Marino, Marcos

    2005-01-01

    The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the ...

  9. Analytic aspects of rational conformal field theories

    International Nuclear Information System (INIS)

    Kiritsis, E.B.; Lawrence Berkeley Lab., CA

    1990-01-01

    The problem of deriving linear differential equations for correlation functions of Rational Conformal Field Theories is considered. Techniques from the theory of fuchsian differential equations are used to show that knowledge of the central charge, dimensions of primary fields and fusion rules are enough to fix the differential equations for one- and two-point functions on the tours. Any other correlation function can be calculated along similar lines. The results settle the issue of 'exact solution' of rational conformal field theories. (orig.)

  10. A Field Theory with Curvature and Anticurvature

    Directory of Open Access Journals (Sweden)

    M. I. Wanas

    2014-01-01

    Full Text Available The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

  11. Gauge field theories an introduction with applications

    CERN Document Server

    Guidry, Mike

    1991-01-01

    Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises

  12. Variational analysis of regular mappings theory and applications

    CERN Document Server

    Ioffe, Alexander D

    2017-01-01

    This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, whic...

  13. Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Doering, C.R.

    1985-01-01

    Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

  14. On single-time reduction in quantum field theory

    International Nuclear Information System (INIS)

    Arkhipov, A.A.

    1984-01-01

    It is shown, how the causality and spectrality properties in qUantum field theory may help one to carry out a single-time reduction of the Bethe-Salpeter wave fUnction. The single-time reduction technique is not based on any concrete model of the quantum field theory. Axiomatic formulations underline the quantum field theory

  15. Analysis and development of stochastic multigrid methods in lattice field theory

    International Nuclear Information System (INIS)

    Grabenstein, M.

    1994-01-01

    We study the relation between the dynamical critical behavior and the kinematics of stochastic multigrid algorithms. The scale dependence of acceptance rates for nonlocal Metropolis updates is analyzed with the help of an approximation formula. A quantitative study of the kinematics of multigrid algorithms in several interacting models is performed. We find that for a critical model with Hamiltonian H(Φ) absence of critical slowing down can only be expected if the expansion of (H(Φ+ψ)) in terms of the shift ψ contains no relevant term (mass term). The predictions of this rule was verified in a multigrid Monte Carlo simulation of the Sine Gordon model in two dimensions. Our analysis can serve as a guideline for the development of new algorithms: We propose a new multigrid method for nonabelian lattice gauge theory, the time slice blocking. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method, in accordance with the theoretical prediction. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems. (orig.)

  16. Phenomenology of noncommutative field theories

    International Nuclear Information System (INIS)

    Carone, C D

    2006-01-01

    Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model

  17. Low dimensional field theories and condensed matter physics

    International Nuclear Information System (INIS)

    Nagaoka, Yosuke

    1992-01-01

    This issue is devoted to the Proceedings of the Fourth Yukawa International Seminar (YKIS '91) on Low Dimensional Field Theories and Condensed Matter Physics, which was held on July 28 to August 3 in Kyoto. In recent years there have been great experimental discoveries in the field of condensed matter physics: the quantum Hall effect and the high temperature superconductivity. Theoretical effort to clarify mechanisms of these phenomena revealed that they are deeply related to the basic problem of many-body systems with strong correlation. On the other hand, there have been important developments in field theory in low dimensions: the conformal field theory, the Chern-Simons gauge theory, etc. It was found that these theories work as a powerful method of approach to the problems in condensed matter physics. YKIS '91 was devoted to the study of common problems in low dimensional field theories and condensed matter physics. The 17 of the presented papers are collected in this issue. (J.P.N.)

  18. Methods of thermal field theory

    Energy Technology Data Exchange (ETDEWEB)

    Mallik, S [Saha Institute of Nuclear Physics, Calcutta (India)

    1998-11-01

    We introduce the basic ideas of thermal field theory and review its path integral formulation. We then discuss the problems of QCD theory at high and at low temperatures. At high temperature the naive perturbation expansion breaks down and is cured by resummation. We illustrate this improved perturbation expansion with the g{sup 2}{phi}{sup 4} theory and then sketch its application to find the gluon damping rate in QCD theory. At low temperature the hadronic phase is described systematically by the chiral perturbation theory. The results obtained from this theory for the quark and the gluon condensates are discussed. (author) 22 refs., 6 figs.

  19. Conformal field theories, Coulomb gas picture and integrable models

    International Nuclear Information System (INIS)

    Zuber, J.B.

    1988-01-01

    The aim of the study is to present the links between some results of conformal field theory, the conventional Coulomb gas picture in statistical mechanics and the approach of integrable models. It is shown that families of conformal theories, related by the coset construction to the SU(2) Kac-Moody algebra, may be regarded as obtained from some free field, and modified by the coupling of its winding numbers to floating charges. This representation reflects the procedure of restriction of the corresponding integrable lattice models. The work may be generalized to models based on the coset construction with higher rank algebras. The corresponding integrable models are identified. In the conformal field description, generalized parafermions appear, and are coupled to free fields living on a higher-dimensional torus. The analysis is not as exhaustive as in the SU(2) case: all the various restrictions have not been identified, nor the modular invariants completely classified

  20. Issues of effective field theories with resonances

    International Nuclear Information System (INIS)

    Gegelia, J.; Japaridze, G.

    2014-01-01

    We address some issues of renormalization and symmetries of effective field theories with unstable particles - resonances. We also calculate anomalous contributions in the divergence of the singlet axial current in an effective field theory of massive SU(N) Yang-Mills fields interacting with fermions and discuss their possible relevance to the strong CP problem. (author)

  1. Analyticity properties of the S-matrix: historical survey and recent results in S-matrix theory and axiomatic field theory

    International Nuclear Information System (INIS)

    Iagolnitzer, D.

    1981-02-01

    An introduction to recent works, in S-matrix theory and axiomatic field theory, on the analysis and derivation of momentum-space analyticity properties of the multiparticle S matrix is presented. It includes an historical survey, which outlines the successes but also the basic difficulties encountered in the sixties in both theories, and the evolution of the subject in the seventies

  2. Effective field theory and the quark model

    International Nuclear Information System (INIS)

    Durand, Loyal; Ha, Phuoc; Jaczko, Gregory

    2001-01-01

    We analyze the connections between the quark model (QM) and the description of hadrons in the low-momentum limit of heavy-baryon effective field theory in QCD. By using a three-flavor-index representation for the effective baryon fields, we show that the 'nonrelativistic' constituent QM for baryon masses and moments is completely equivalent through O(m s ) to a parametrization of the relativistic field theory in a general spin-flavor basis. The flavor and spin variables can be identified with those of effective valence quarks. Conversely, the spin-flavor description clarifies the structure and dynamical interpretation of the chiral expansion in effective field theory, and provides a direct connection between the field theory and the semirelativistic models for hadrons used in successful dynamical calculations. This allows dynamical information to be incorporated directly into the chiral expansion. We find, for example, that the striking success of the additive QM for baryon magnetic moments is a consequence of the relative smallness of the non-additive spin-dependent corrections

  3. String fields, higher spins and number theory

    CERN Document Server

    Polyakov, Dimitri

    2018-01-01

    The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.

  4. Two field formulation of closed string field theory

    International Nuclear Information System (INIS)

    Bogojevic, A.R.

    1990-09-01

    A formulation of closed string field theory is presented that is based on a two field action. It represents a generalization of Witten's Chern-Simons formulation of 3d gravity. The action contains only 3 string interactions and no string field truncations, unlike the previous non-polynomial action of Zwiebach. The two field action is found to follow from a purely cubic, background independent action similar to the one for open strings. (orig.)

  5. Nilpotent weights in conformal field theory

    Directory of Open Access Journals (Sweden)

    S. Rouhani

    2001-12-01

    Full Text Available   Logarithmic conformal field theory can be obtained using nilpotent weights. Using such scale transformations various properties of the theory were derived. The derivation of four point function needs a knowledge of singular vectors which is derived by including nilpotent variables into the Kac determinant. This leads to inhomogeneous hypergeometric functions. Finally we consider the theory near a boundary and also introduce the concept of superfields where a multiplet of conformal fields are dealt with together. This leads to the OPE of superfields and a logarithmic partner for the energy momentum tensor.

  6. Schrodinger representation in renormalizable quantum field theory

    International Nuclear Information System (INIS)

    Symanzik, K.

    1983-01-01

    The problem of the Schrodinger representation arose from work on the Nambu-Goto Ansatz for integration over surfaces. Going beyond semiclassical approximation leads to two problems of nonrenormalizibility and of whether Dirichlet boundary conditions can be imposed on a ''Euclidean'' quantum field theory. The Schrodinger representation is constructed in a way where the principles of general renormalization theory can be refered to. The Schrodinger function of surface terms is studied, as well as behaviour at the boundary. The Schrodinger equation is derived. Completeness, unitarity, and computation of expectation values are considered. Extensions of these methods into other Bose field theories such as Fermi fields and Marjorana fields is straightforward

  7. An introduction to conformal field theory

    International Nuclear Information System (INIS)

    Zuber, J.B.

    1995-01-01

    The aim of these lectures is to present an introduction at a fairly elementary level to recent developments in two dimensional field theory, namely in conformal field theory. We shall see the importance of new structures related to infinite dimensional algebras: current algebras and Virasoro algebra. These topics will find physically relevant applications in the lectures by Shankar and Ian Affeck. (author)

  8. A general action for topological quantum field theories

    International Nuclear Information System (INIS)

    Dayi, O.F.

    1989-03-01

    Topological field theories can be formulated by beginning from a higher dimensional action. The additional dimension is an unphysical time parameter and the action is the derivative of a functional W with respect to this variable. In the d = 4 case, it produces actions which are shown to give topological quantum field theory after gauge fixing. In d = 3 this action leads to the Hamiltonian, which yields the Floer groups if the additional parameter is treated as physical when W is the pure Chern-Simons action. This W can be used to define a topological quantum field theory in d = 3 by treating the additional parameter as unphysical. The BFV-BRST operator quantization of this theory yields to an enlarged system which has only first class constraints. This is not identical to the previously introduced d = 3 topological quantum field theory, even if it is shown that the latter theory also gives the theory which we began with, after a partial gauge fixing. (author). 18 refs

  9. On the interplay between string theory and field theory

    International Nuclear Information System (INIS)

    Brunner, I.

    1998-01-01

    In this thesis, we have discussed various aspects of branes in string theory and M-theory. In chapter 2 we were able to construct six-dimensional chiral interacting eld theories from Hanany-Witten like brane setups. The field theory requirement that the anomalies cancel was reproduced by RR-charge conservation in the brane setup. The data of the Hanany-Witten setup, which consists of brane positions, was mapped to instanton data. The orbifold construction can be extended to D and E type singularities. In chapter 3 we discussed a matrix conjecture, which claims that M-theory in the light cone gauge is described by the quantum mechanics of D0 branes. Toroidal compactifications of M-theory have a description in terms of super Yang-Mills theory an the dual torus. For more than three compactified dimensions, more degrees of freedom have to be added. In some sense, the philosophy in this chapter is orthogonal to the previous chapter: Here, we want to get M-theory results from eld theory considerations, whereas in the previous chapter we obtained eld theory results by embedding the theories in string theory. Our main focus was on the compactification on T 6 , which leads to complications. Here, the Matrix model is again given by an eleven dimensional theory, not by a lower dimensional field theory. Other problems and possible resolutions of Matrix theory are discussed at the end of chapter 3. In the last chapter we considered M- and F-theory compactifications on Calabi-Yau fourfolds. After explaining some basics of fourfolds, we showed that the web of fourfolds is connected by singular transitions. The two manifolds which are connected by the transition are different resolutions of the same singular manifold. The resolution of the singularities can lead to a certain type of divisors, which lead to non-perturbative superpotentials, when branes wrap them. The vacua connected by the transitions can be physically very different. (orig.)

  10. On the interplay between string theory and field theory

    Energy Technology Data Exchange (ETDEWEB)

    Brunner, I.

    1998-07-08

    In this thesis, we have discussed various aspects of branes in string theory and M-theory. In chapter 2 we were able to construct six-dimensional chiral interacting eld theories from Hanany-Witten like brane setups. The field theory requirement that the anomalies cancel was reproduced by RR-charge conservation in the brane setup. The data of the Hanany-Witten setup, which consists of brane positions, was mapped to instanton data. The orbifold construction can be extended to D and E type singularities. In chapter 3 we discussed a matrix conjecture, which claims that M-theory in the light cone gauge is described by the quantum mechanics of D0 branes. Toroidal compactifications of M-theory have a description in terms of super Yang-Mills theory an the dual torus. For more than three compactified dimensions, more degrees of freedom have to be added. In some sense, the philosophy in this chapter is orthogonal to the previous chapter: Here, we want to get M-theory results from eld theory considerations, whereas in the previous chapter we obtained eld theory results by embedding the theories in string theory. Our main focus was on the compactification on T{sup 6}, which leads to complications. Here, the Matrix model is again given by an eleven dimensional theory, not by a lower dimensional field theory. Other problems and possible resolutions of Matrix theory are discussed at the end of chapter 3. In the last chapter we considered M- and F-theory compactifications on Calabi-Yau fourfolds. After explaining some basics of fourfolds, we showed that the web of fourfolds is connected by singular transitions. The two manifolds which are connected by the transition are different resolutions of the same singular manifold. The resolution of the singularities can lead to a certain type of divisors, which lead to non-perturbative superpotentials, when branes wrap them. The vacua connected by the transitions can be physically very different. (orig.)

  11. Brane configurations and 4D field theory dualities

    International Nuclear Information System (INIS)

    Brandhuber, A.; Sonnenschein, J.; Yankielowicz, S.

    1997-01-01

    We study brane configurations which correspond to field theories in four dimension with N=2 and N=1 supersymmetry. In particular we discuss brane motions that translate to Seiberg's duality in N=1 models recently studied by Elitzur, Giveon and Kutasov. We investigate, using the brane picture, the moduli spaces of the dual theories. Deformations of these models like mass terms and vacuum expectation values of scalar fields can be identified with positions of branes. The map of these deformations between the electric and dual magnetic theories is clarified. The models we study reproduce known field theory results and we provide an example of new dual pairs with N=1 supersymmetry. Possible relations between brane configurations and non-supersymmetric field theories are discussed. (orig.)

  12. Mean-field magnetohydrodynamics and dynamo theory

    CERN Document Server

    Krause, F

    2013-01-01

    Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen

  13. Spectral methods in quantum field theory

    International Nuclear Information System (INIS)

    Graham, Noah; Quandt, Markus; Weigel, Herbert

    2009-01-01

    This concise text introduces techniques from quantum mechanics, especially scattering theory, to compute the effects of an external background on a quantum field in general, and on the properties of the quantum vacuum in particular. This approach can be succesfully used in an increasingly large number of situations, ranging from the study of solitons in field theory and cosmology to the determination of Casimir forces in nano-technology. The method introduced and applied in this book is shown to give an unambiguous connection to perturbation theory, implementing standard renormalization conditions even for non-perturbative backgrounds. It both gives new theoretical insights, for example illuminating longstanding questions regarding Casimir stresses, and also provides an efficient analytic and numerical tool well suited to practical calculations. Last but not least, it elucidates in a concrete context many of the subtleties of quantum field theory, such as divergences, regularization and renormalization, by connecting them to more familiar results in quantum mechanics. While addressed primarily at young researchers entering the field and nonspecialist researchers with backgrounds in theoretical and mathematical physics, introductory chapters on the theoretical aspects of the method make the book self-contained and thus suitable for advanced graduate students. (orig.)

  14. Background Independent Open String Field Theory and Constant B-Field

    OpenAIRE

    Nemeschansky, D.; Yasnov, V.

    2000-01-01

    We calculate the background independent action for bosonic and supersymmetric open string field theory in a constant B-field. We also determine the tachyon effective action in the presence of constant B-field.

  15. 2D conformal field theories and holography

    International Nuclear Information System (INIS)

    Freidel, Laurent; Krasnov, Kirill

    2004-01-01

    It is known that the chiral part of any 2D conformal field theory defines a 3D topological quantum field theory: quantum states of this TQFT are the CFT conformal blocks. The main aim of this paper is to show that a similar CFT/TQFT relation exists also for the full CFT. The 3D topological theory that arises is a certain 'square' of the chiral TQFT. Such topological theories were studied by Turaev and Viro; they are related to 3D gravity. We establish an operator/state correspondence in which operators in the chiral TQFT correspond to states in the Turaev-Viro theory. We use this correspondence to interpret CFT correlation functions as particular quantum states of the Turaev-Viro theory. We compute the components of these states in the basis in the Turaev-Viro Hilbert space given by colored 3-valent graphs. The formula we obtain is a generalization of the Verlinde formula. The later is obtained from our expression for a zero colored graph. Our results give an interesting 'holographic' perspective on conformal field theories in two dimensions

  16. Non-local charges in local quantum field theory

    International Nuclear Information System (INIS)

    Buchholz, D.; Lopuszanski, J.T.; Rabsztyn, S.

    1985-05-01

    Non-local charges are studied in the general setting of local quantum field theory. It is shown, that these charges can be represented as polynomials in the incoming respectively outgoing fields with coefficients (kernels) which are subject to specific constraints. For the restricted class of models of a scalar, massive, self interacting particle in four dimensions, a more detailed analysis shows that all non-local charges of the generic type (genus 2) are products of generators of the Poincare group. This analysis, which is based on the macroscopic causality properties of the S-matrix, seems to indicate that less trivial examples of non-local charges can only exist in two dimensions. (orig.)

  17. Experimental signature of scaling violation implied by field theories

    International Nuclear Information System (INIS)

    Tung, W.

    1975-01-01

    Renormalizable field theories are found to predict a surprisingly specific pattern of scaling violation in deep inelastic scattering. Comparison with experiments is discussed. The feasibility of distinguishing asymptotically free field theories from conventional field theories is evaluated

  18. Gyrokinetic field theory

    International Nuclear Information System (INIS)

    Sugama, H.

    1999-08-01

    The Lagrangian formulation of the gyrokinetic theory is generalized in order to describe the particles' dynamics as well as the self-consistent behavior of the electromagnetic fields. The gyrokinetic equation for the particle distribution function and the gyrokinetic Maxwell's equations for the electromagnetic fields are both derived from the variational principle for the Lagrangian consisting of the parts of particles, fields, and their interaction. In this generalized Lagrangian formulation, the energy conservation property for the total nonlinear gyrokinetic system of equations is directly shown from the Noether's theorem. This formulation can be utilized in order to derive the nonlinear gyrokinetic system of equations and the rigorously conserved total energy for fluctuations with arbitrary frequency. (author)

  19. Conformal invariant quantum field theory and composite field operators

    International Nuclear Information System (INIS)

    Kurak, V.

    1976-01-01

    The present status of conformal invariance in quantum field theory is reviewed from a non group theoretical point of view. Composite field operators dimensions are computed in some simple models and related to conformal symmetry

  20. High energy approximations in quantum field theory

    International Nuclear Information System (INIS)

    Orzalesi, C.A.

    1975-01-01

    New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given [pt

  1. Using field theory in hadron physics

    International Nuclear Information System (INIS)

    Abarbanel, H.D.I.

    1979-01-01

    The author gives an introductory review about the development of applications of quantum field theory in hadron physics. Especially he discusses the renormalization group and the use of this group for the selection of a field theory. In this framework he compares quantum chromodynamics with quantum electrodynamics. Finally he discusses dynamic mass generation and quark confinement in the framework of quantum chromodynamics. (HSI) [de

  2. Non-commutative field theory with twistor-like coordinates

    International Nuclear Information System (INIS)

    Taylor, Tomasz R.

    2007-01-01

    We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared-ultraviolet mixing problem

  3. Twistors and four-dimensional conformal field theory

    International Nuclear Information System (INIS)

    Singer, M.A.

    1990-01-01

    This is a report (with technical details omitted) on work concerned with generalizations to four dimensions of two-dimensional Conformed Field Theory. Accounts of this and related material are contained elsewhere. The Hilbert space of the four-dimensional theory has a natural interpretation in terms of massless spinor fields on real Minkowski space. From the twistor point of view this follows from the boundary CR-manifold P being precisely the space of light rays in real compactified Minkowski space. All the amplitudes can therefore be regarded as defined on Hilbert spaces built from Lorentzian spinor fields. Thus the twistor picture provides a kind of halfway house between the Lorentzian and Euclidean field theories. (author)

  4. Compositional Data Analysis Theory and Applications

    CERN Document Server

    Pawlowsky-Glahn, Vera

    2011-01-01

    This book presents the state-of-the-art in compositional data analysis and will feature a collection of papers covering theory, applications to various fields of science and software. Areas covered will range from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. Key features:Provides the state-of-the-art text in compositional data analysisCovers a variety of subject areas, from geology to medicineWritten by leading researchers in the fieldIs supported by a website featuring R code

  5. Group field theories for all loop quantum gravity

    Science.gov (United States)

    Oriti, Daniele; Ryan, James P.; Thürigen, Johannes

    2015-02-01

    Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

  6. Superstring field theory equivalence: Ramond sector

    International Nuclear Information System (INIS)

    Kroyter, Michael

    2009-01-01

    We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.

  7. Abelian gauge theories with tensor gauge fields

    International Nuclear Information System (INIS)

    Kapuscik, E.

    1984-01-01

    Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)

  8. Coadjoint orbits and conformal field theory

    International Nuclear Information System (INIS)

    Taylor, W. IV.

    1993-08-01

    This thesis is primarily a study of certain aspects of the geometric and algebraic structure of coadjoint orbit representations of infinite-dimensional Lie groups. The goal of this work is to use coadjoint orbit representations to construct conformal field theories, in a fashion analogous to the free-field constructions of conformal field theories. The new results which are presented in this thesis are as follows: First, an explicit set of formulae are derived giving an algebraic realization of coadjoint orbit representations in terms of differential operators acting on a polynomial Fock space. These representations are equivalent to dual Verma module representations. Next, intertwiners are explicitly constructed which allow the construction of resolutions for irreducible representations using these Fock space realizations. Finally, vertex operators between these irreducible representations are explicitly constructed as chain maps between the resolutions; these vertex operators allow the construction of rational conformal field theories according to an algebraic prescription

  9. Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation

    CERN Document Server

    Scheck, Florian

    2012-01-01

    The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...

  10. Clifford algebra in finite quantum field theories

    International Nuclear Information System (INIS)

    Moser, M.

    1997-12-01

    We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)

  11. Noncommutative time in quantum field theory

    International Nuclear Information System (INIS)

    Salminen, Tapio; Tureanu, Anca

    2011-01-01

    We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-Kaellen equation), and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of lightlike noncommutativity.

  12. Topological defects in open string field theory

    Science.gov (United States)

    Kojita, Toshiko; Maccaferri, Carlo; Masuda, Toru; Schnabl, Martin

    2018-04-01

    We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.

  13. Magnetic charge in an octonionic field theory

    International Nuclear Information System (INIS)

    Lassig, C.C.; Jashi, G.C.

    1996-01-01

    The violation of the Jacobi identity by the presence of magnetic charge is accommodated by using an explicitly nonassociative theory of octonionic fields. Lagrangian and Hamiltonian formalisms are constructed, and issues of the quantisation discussed. Finally an extension of these concepts to string theory is contemplated. The two main problems that seems to arise in this octonionic field theory are the difficulty of constructing an appropriate action to suit the desired equations of motion, and the failure to complete a Hamiltonian formalism and hence quantize the theory. 8 refs

  14. The conceptual framework of quantum field theory

    CERN Document Server

    Duncan, Anthony

    2012-01-01

    The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The "Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quan...

  15. Path operator algebras in conformal quantum field theories

    International Nuclear Information System (INIS)

    Roesgen, M.

    2000-10-01

    Two different kinds of path algebras and methods from noncommutative geometry are applied to conformal field theory: Fusion rings and modular invariants of extended chiral algebras are analyzed in terms of essential paths which are a path description of intertwiners. As an example, the ADE classification of modular invariants for minimal models is reproduced. The analysis of two-step extensions is included. Path algebras based on a path space interpretation of character identities can be applied to the analysis of fusion rings as well. In particular, factorization properties of character identities and therefore of the corresponding path spaces are - by means of K-theory - related to the factorization of the fusion ring of Virasoro- and W-algebras. Examples from nonsupersymmetric as well as N=2 supersymmetric minimal models are discussed. (orig.)

  16. Super-Galilei invariant field theories in 2+1 dimensions

    International Nuclear Information System (INIS)

    Bergman, O.; Thorn, C.B.

    1995-01-01

    The authors extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. They also study the generalization to matrix valued fields, which are relevant to the formulation of superstring theory as a 1/N c expansion of a field theory. The authors find that in the matrix case, the field theory is much more restricted by the supersymmetry

  17. Lectures on classical and quantum theory of fields

    International Nuclear Information System (INIS)

    Arodz, Henryk; Hadasz, Leszek

    2010-01-01

    This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)

  18. Lectures on Classical and Quantum Theory of Fields

    CERN Document Server

    Arodź, Henryk

    2010-01-01

    This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

  19. Lectures on classical and quantum theory of fields

    Energy Technology Data Exchange (ETDEWEB)

    Arodz, Henryk; Hadasz, Leszek [Jagiellonian Univ., Krakow (Poland). Inst. Physics

    2010-07-01

    This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)

  20. Infrared problems in field perturbation theory

    International Nuclear Information System (INIS)

    David, Francois.

    1982-12-01

    The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr

  1. Antisymmetric tensor Zp gauge symmetries in field theory and string theory

    International Nuclear Information System (INIS)

    Berasaluce-González, Mikel; Ramírez, Guillermo; Uranga, Angel M.

    2014-01-01

    We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general Z p gauge theory can be described in terms of a r-form gauge field made massive by a (r−1)-form, or other dual realizations, that we also discuss. The theory contains charged topological defects of different dimensionalities, generalizing the familiar charged particles and strings in D=4. We describe realizations in string theory compactifications with torsion cycles, or with background field strength fluxes. We also provide examples of non-abelian discrete groups, for which the group elements are associated with charged objects of different dimensionality

  2. Coherent states field theory in supramolecular polymer physics

    Science.gov (United States)

    Fredrickson, Glenn H.; Delaney, Kris T.

    2018-05-01

    In 1970, Edwards and Freed presented an elegant representation of interacting branched polymers that resembles the coherent states (CS) formulation of second-quantized field theory. This CS polymer field theory has been largely overlooked during the intervening period in favor of more conventional "auxiliary field" (AF) interacting polymer representations that form the basis of modern self-consistent field theory (SCFT) and field-theoretic simulation approaches. Here we argue that the CS representation provides a simpler and computationally more efficient framework than the AF approach for broad classes of reversibly bonding polymers encountered in supramolecular polymer science. The CS formalism is reviewed, initially for a simple homopolymer solution, and then extended to supramolecular polymers capable of forming reversible linkages and networks. In the context of the Edwards model of a non-reacting homopolymer solution and one and two-component models of telechelic reacting polymers, we discuss the structure of CS mean-field theory, including the equivalence to SCFT, and show how weak-amplitude expansions (random phase approximations) can be readily developed without explicit enumeration of all reaction products in a mixture. We further illustrate how to analyze CS field theories beyond SCFT at the level of Gaussian field fluctuations and provide a perspective on direct numerical simulations using a recently developed complex Langevin technique.

  3. Problems of an external field in non-Abelian gauge theory

    International Nuclear Information System (INIS)

    Gavrilov, S.P.; Gitman, D.M.

    1992-01-01

    In the Abelian gauge field theory QED the principal problems connected with an external field are the problems of exact keeping of an external field in a perturbation theory and appearing in this case the peculiarities of the theory such as the instability of the vacuum and so on. There is the problem of an external field introduction or its interpretation side by side with this problem in Non-Abelian gauge theory. The solution of both these problems in Non-Abelian theory can be considered by analogy with QED. In the present paper, the authors discuss on the example of the spontaneously broken SU(2) x U(1) electroweak theory both the problems of an external field introduction and the problem of exact keeping of this field in the perturbation theory. The Langrangian of this theory in covariant gauge is chosen in the BRST invariant form. In spite of concrete character of the theory studied, the method can be extended to any gauge theory

  4. Quantum field theory and the standard model

    CERN Document Server

    Schwartz, Matthew D

    2014-01-01

    Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of clear physical explanations, with direct connections to experimental data, and mathematical rigor make the subject accessible to students with a wide variety of backgrounds and interests. Assuming only an undergraduate-level understanding of quantum mechanics, the book steadily develops the Standard Model and state-of-the-art calculation techniques. It includes multiple derivations of many important results, with modern methods such as effective field theory and the renormalization group playing a prominent role. Numerous worked examples and end-of-chapter problems enable students to reproduce classic results and to master quantum field theory as it is used today. Based on a course taught by the author over many years, this book is ideal for an introductory to advanced quantum field theory sequence or for independe...

  5. Irreversibility and higher-spin conformal field theory

    CERN Document Server

    Anselmi, D

    2000-01-01

    I discuss the idea that quantum irreversibility is a general principle of nature and a related "conformal hypothesis", stating that all fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points. In particular, the Newton constant should be viewed as a low-energy effect of the RG scale. This approach leads naturally to consider higher-spin conformal field theories, which are here classified, as candidate high-energy theories. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. The central charges c and a are well defined and positive. I calculate their values and study the operator-product structure. Fermionic theories have no gauge invariance and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a...

  6. Finite spatial volume approach to finite temperature field theory

    International Nuclear Information System (INIS)

    Weiss, Nathan

    1981-01-01

    A relativistic quantum field theory at finite temperature T=β -1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned. (auth)

  7. Topics in field theory-higher spins, CFT, and gravity

    International Nuclear Information System (INIS)

    Yang, Z.

    1990-01-01

    Several topics in field theory are investigated. (1) Massive higher spin actions are obtained as gauge theories from the dimensional reduction of the corresponding massless ones. (2) The author considers a model of spin4 and spin2 interaction through the Bel-Robinson tensor of spin2 field, which in conserved at free level. The coupling is inconsistent, yet there are indications that adding still higher spin couplings would be a promising direction to achieve consistency. (3) Energy and Stability of Einstein-Gauss-Bonnet models of gravity are studied. It is shown that flat space is stable while AdS is not. (4) Gauged Wess-Zumino-Witten models are studied in detail. The equivalence to GKO construction of conformal field theory is considered. BRST quantization of the models is given. (5) Nonrenormalizability of quantum gravity is, in the binomial first order metric formulation, traced to a mismatch between the symmetries of its quadratic and cubic term. (6) The possibility that the gravitational model defined in D = 3 by an action which is the sum of Einstein and Chern-Simons terms is a viable quantum theory is investigated. It is shown that it is compatible with power-counting renormalizability. Gauge invariant regularizations, however, have not been found to exist. Detailed BRS analysis shows that there are possible anomalies

  8. Teleparallel Lagrange geometry and a unified field theory

    Energy Technology Data Exchange (ETDEWEB)

    Wanas, M I [Department of Astronomy, Faculty of Science, Cairo University, CTP of the British University in Egypt (BUE) (Egypt); Youssef, Nabil L; Sid-Ahmed, A M, E-mail: wanas@frcu.eun.eg, E-mail: nyoussef@frcu.eun.e, E-mail: nlyoussef2003@yahoo.f, E-mail: amrs@mailer.eun.e, E-mail: amrsidahmed@gmail.co [Department of Mathematics, Faculty of Science, Cairo University (Egypt)

    2010-02-21

    In this paper, we construct a field theory unifying gravity and electromagnetism in the context of extended absolute parallelism (EAP) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and the mathematical simplicity of absolute parallelism (AP) geometry. The constructed field theory is a generalization of the generalized field theory (GFT) formulated by Mikhail and Wanas. The theory obtained is purely geometric. The horizontal (resp. vertical) field equations are derived by applying the Euler-Lagrange equations to an appropriate horizontal (resp. vertical) scalar Lagrangian. The symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Einstein's field equations in which the horizontal (resp. vertical) energy-momentum tensor is purely geometric. The skew-symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Maxwell equations in which the electromagnetic field is purely geometric. Some interesting special cases, which reveal the role of the nonlinear connection in the obtained field equations, are examined. Finally, the condition under which our constructed field equations reduce to the GFT is explicitly established.

  9. Could reggeon field theory be an effective theory for QCD in the Regge limit?

    Energy Technology Data Exchange (ETDEWEB)

    Bartels, Jochen [II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg (Germany); Contreras, Carlos [Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Avda. España 1680, Casilla 110-V, Valparaiso (Chile); Vacca, G.P. [INFN Sezione di Bologna, DIFA, Via Irnerio 46, I-40126 Bologna (Italy)

    2016-03-30

    In this paper we investigate the possibility whether, in the extreme limit of high energies and large transverse distances, reggeon field theory might serve as an effective theory of high energy scattering for strong interactions. We analyse the functional renormalization group equations (flow equations) of reggeon field theory and search for fixed points in the space of (local) reggeon field theories. We study in complementary ways the candidate for the scaling solution, investigate its main properties and briefly discuss possible physical interpretations.

  10. Infrared behavior of massless field theories

    International Nuclear Information System (INIS)

    Sapirstein, J.R.

    1979-01-01

    Typical infrared effects in several gauge field theories with massless particles are investigated in perturbation theory. It is first shown that divergences occurring in individual Feynman graphs arising from integrations over the long-wavelength modes of the fields cancel when the graphs are grouped together in a particular way, in a generalization of the Bloch-Nordsieck treatment of QED. As one of the requirements of finiteness is renormalization of the vector propagator off shell, the charge in these theories is not directly related to classical experiment. In an effort to find the meaning of charge the low-energy theorem is considered. Although in lowest order the graphs reproduce the Thompson limit, it is found that loop corrections are singular in the low-energy limit; a simple definition of the charge is thus precluded. Finally, the behavior of the quark color magnetic moment is treated. An apparent infrared singularity of this moment is shown to be due to an improper use of perturbation theory, and is removed and replaced with a finite, field-dependent moment, by use of Furry picture propagators

  11. Effective field theory for magnetic compactifications

    Energy Technology Data Exchange (ETDEWEB)

    Buchmuller, Wilfried; Dierigl, Markus [Deutsches Elektronen-Synchrotron DESY,22607 Hamburg (Germany); Dudas, Emilian [Centre de Physique Théorique, École Polytechnique, CNRS, Université Paris-Saclay,F-91128 Palaiseau (France); Schweizer, Julian [Deutsches Elektronen-Synchrotron DESY,22607 Hamburg (Germany)

    2017-04-10

    Magnetic flux plays an important role in compactifications of field and string theories in two ways, it generates a multiplicity of chiral fermion zero modes and it can break supersymmetry. We derive the complete four-dimensional effective action for N=1 supersymmetric Abelian and non-Abelian gauge theories in six dimensions compactified on a torus with flux. The effective action contains the tower of charged states and it accounts for the mass spectrum of bosonic and fermionic fields as well as their level-dependent interactions. This allows us to compute quantum corrections to the mass and couplings of Wilson lines. We find that the one-loop corrections vanish, contrary to the case without flux. This can be traced back to the spontaneous breaking of symmetries of the six-dimensional theory by the background gauge field, with the Wilson lines as Goldstone bosons.

  12. Chiral gauged Wess-Zumino-Witten theories and coset models in conformal field theory

    International Nuclear Information System (INIS)

    Chung, S.; Tye, S.H.

    1993-01-01

    The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by G L direct-product G R . In the standard gauged WZW theory, vector gauge fields (i.e., with vector gauge couplings) are in the adjoint representation of the subgroup H contained-in G. In this paper, we show that, in the conformal limit in two dimensions, there is a gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R where H L and H R can be different groups. In the special case where H L =H R , the theory is equivalent to vector gauged WZW theory. For general groups H L and H R , an examination of the correlation functions (or more precisely, conformal blocks) shows that the chiral gauged WZW theory is equivalent to (G/H L ) L direct-product(G/H R ) R coset models in conformal field theory

  13. Non-topological solitons in field theories with kinetic self-coupling

    International Nuclear Information System (INIS)

    Diaz-Alonso, Joaquin; Rubiera-Garcia, Diego

    2007-01-01

    We investigate some fundamental features of a class of non-linear relativistic Lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication

  14. Smooth massless limit of field theories

    International Nuclear Information System (INIS)

    Fronsdal, C.

    1980-01-01

    The massless limit of Fierz-Pauli field theories, describing fields with fixed mass and spin interacting with external sources, is examined. Results are obtained for spins, 1, 3/2, 2 and 3 using conventional models, and then for all half-integral spins in a relatively model-independent manner. It is found that the massless limit is smooth provided that the sources satisfy certain conditions. In the massless limit these conditions reduce to the conservation laws required by internal consistency of massless field theory. Smoothness simply requires that quantities that vanish in the massless case approach zero in a certain well-defined manner. (orig.)

  15. Phase-space quantization of field theory

    International Nuclear Information System (INIS)

    Curtright, T.; Zachos, C.

    1999-01-01

    In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999

  16. Solving topological field theories on mapping tori

    International Nuclear Information System (INIS)

    Blau, M.; Jermyn, I.; Thompson, G.

    1996-05-01

    Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1 modul 1) model of Rozansky and Saleur on Σ x S 1 , both directly and using equivalent two-dimensional theories. We also derive the partition function on a certain non-abelian generalization of the U(1 modul 1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two- dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold. (author). 20 refs

  17. Introduction to field theory of strings

    International Nuclear Information System (INIS)

    Kikkawa, K.

    1987-01-01

    The field theory of bosonic string is reviewed. First, theory is treated in a light-cone gauge. After a brief survey of the first quantized theory of free string, the second quantization is discussed. All possible interactions of strings are introduced based on a smoothness condition of work sheets swept out by strings. Perturbation theory is developed. Finally a possible way to the manifest covariant formalism is discussed

  18. Playing with QCD I: effective field theories

    International Nuclear Information System (INIS)

    Fraga, Eduardo S.

    2009-01-01

    The building blocks of hadrons are quarks and gluons, although color is confined into singlet states. QCD is believed to be the fundamental theory of strong interactions. Its asymptotically free nature puts the vacuum out of reach for perturbation theory. The Lagrangian of QCD and the Feynman rules associated were built by using the Gauge Principle, starting from the quark matter fields and obtaining gluons as connections. A simpler, and sometimes necessary or complementary, approach is provided by effective field theories or effective models, especially when one has to deal with the nonperturbative sector of the theory. (author)

  19. Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits

    Energy Technology Data Exchange (ETDEWEB)

    Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics

    1975-03-01

    General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.

  20. String field theory. Algebraic structure, deformation properties and superstrings

    International Nuclear Information System (INIS)

    Muenster, Korbinian

    2013-01-01

    This thesis discusses several aspects of string field theory. The first issue is bosonic open-closed string field theory and its associated algebraic structure - the quantum open-closed homotopy algebra. We describe the quantum open-closed homotopy algebra in the framework of homotopy involutive Lie bialgebras, as a morphism from the loop homotopy Lie algebra of closed string to the involutive Lie bialgebra on the Hochschild complex of open strings. The formulation of the classical/quantum open-closed homotopy algebra in terms of a morphism from the closed string algebra to the open string Hochschild complex reveals deformation properties of closed strings on open string field theory. In particular, we show that inequivalent classical open string field theories are parametrized by closed string backgrounds up to gauge transformations. At the quantum level the correspondence is obstructed, but for other realizations such as the topological string, a non-trivial correspondence persists. Furthermore, we proof the decomposition theorem for the loop homotopy Lie algebra of closed string field theory, which implies uniqueness of closed string field theory on a fixed conformal background. Second, the construction of string field theory can be rephrased in terms of operads. In particular, we show that the formulation of string field theory splits into two parts: The first part is based solely on the moduli space of world sheets and ensures that the perturbative string amplitudes are recovered via Feynman rules. The second part requires a choice of background and determines the real string field theory vertices. Each of these parts can be described equivalently as a morphism between appropriate cyclic and modular operads, at the classical and quantum level respectively. The algebraic structure of string field theory is then encoded in the composition of these two morphisms. Finally, we outline the construction of type II superstring field theory. Specific features of the

  1. Matrix models as non-commutative field theories on R3

    International Nuclear Information System (INIS)

    Livine, Etera R

    2009-01-01

    In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as generalized matrix models. Focusing on 2d group field theories, we review their explicit relation to matrix models and show their link to a class of non-commutative field theories invariant under a quantum-deformed 3d Poincare symmetry. This provides a simple relation between matrix models and non-commutative geometry. Moreover, we review the derivation of effective 2d group field theories with non-trivial propagators from Boulatov's group field theory for 3d quantum gravity. Besides the fact that this gives a simple and direct derivation of non-commutative field theories for the matter dynamics coupled to (3d) quantum gravity, these effective field theories can be expressed as multi-matrix models with a non-trivial coupling between matrices of different sizes. It should be interesting to analyze this new class of theories, both from the point of view of matrix models as integrable systems and for the study of non-commutative field theories.

  2. Transversity results and computations in symplectic field theory

    International Nuclear Information System (INIS)

    Fabert, Oliver

    2008-01-01

    Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M φ of symplectic manifolds (M,ω M ) with symplectomorphisms φ. While the cylindrical contact homology of M φ is given by the Floer homologies of powers of φ, the other algebraic invariants of symplectic field theory for M φ provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian φ we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M φ ≅ S 1 x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic field theory are established, our result implies that the

  3. Mean-field theory of nuclear structure and dynamics

    International Nuclear Information System (INIS)

    Negele, J.W.

    1982-01-01

    The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission

  4. Exotic dual of type II double field theory

    Directory of Open Access Journals (Sweden)

    Eric A. Bergshoeff

    2017-04-01

    Full Text Available We perform an exotic dualization of the Ramond–Ramond fields in type II double field theory, in which they are encoded in a Majorana–Weyl spinor of O(D,D. Starting from a first-order master action, the dual theory in terms of a tensor–spinor of O(D,D is determined. This tensor–spinor is subject to an exotic version of the (self-duality constraint needed for a democratic formulation. We show that in components, reducing O(D,D to GL(D, one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, such as the 4-form in type IIB string theory.

  5. Introduction to field theory

    CERN Multimedia

    CERN. Geneva; CERN. Geneva

    2001-01-01

    Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero spacetime dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four spacetime dimensions, and the full Feynman rules for relativisitc scalar theory derived. The S matrix and the concept of unitarity are discussed, leading to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.

  6. Half-maximal supersymmetry from exceptional field theory

    Energy Technology Data Exchange (ETDEWEB)

    Malek, Emanuel [Arnold Sommerfeld Center for Theoretical Physics, Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen (Germany)

    2017-10-15

    We study D ≥ 4-dimensional half-maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half-maximal Minkowski{sub D} and AdS{sub D} vacua. We then show how to obtain consistent truncations of type II / 11-dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised SO(d - 1 - N) structures, where d = 11 - D, and N is the number of vector multiplets obtained in the lower-dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half-maximal gauged SUGRA. We use this to prove that all D ≥ 4 half-maximal warped AdS{sub D} and Minkowski{sub D} vacua of type II / 11-dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M-theory / heterotic duality. In five dimensions, we find a new SO(5, N) double field theory with a (6 + N)-dimensional extended space. Its section condition has one solution corresponding to 10-dimensional N = 1 supergravity and another yielding six-dimensional N = (2, 0) SUGRA. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  7. Topological Field Theory of Time-Reversal Invariant Insulators

    Energy Technology Data Exchange (ETDEWEB)

    Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.

    2010-03-19

    We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.

  8. On the general theory of quantized fields

    International Nuclear Information System (INIS)

    Fredenhagen, K.

    1991-10-01

    In my lecture I describe the present stage of the general theory of quantized fields on the example of 5 subjects. They are ordered in the direction from large to small distances. The first one is the by now classical problem of the structure of superselection sectors. It involves the behavior of the theory at spacelike infinity and is directly connected with particle statistics and internal symmetries. It has become popular in recent years by the discovery of a lot of nontrivial models in 2d conformal-field theory, by connections to integrable models and critical behavior in statistical mechanics and by the relations to the Jones' theory of subfactors in von Neumann algebras and to the corresponding geometrical objects (braids, knots, 3d manifolds, ...). At large timelike distances the by far most important feature of quantum field theory is the particle structure. This will be the second subject of my lecture. It follows the technically most involved part which is concerned with the behavior at finite distances. Two aspets, nuclearity which emphasizes the finite density of states in phase space, and the modular structure which relies on the infinite number of degrees of freedom present even locally, and their mutual relations will be treated. The next point, involving the structure at infinitesimal distances, is the connection between the Haag-Kastler framework of algebras of local and the framework of Wightman fields. Finally, problems in approaches to quantum gravity will be discussed, as far as they are accessible by the methods of the general theory of quantized fields. (orig.)

  9. Parafermionic conformal field theory

    International Nuclear Information System (INIS)

    Kurak, V.

    1989-09-01

    Conformal parafermionic field theories are reviewed with emphasis on the computation of their OPE estructure constants. It is presented a simple computational of these for the Z(N) parafermions, unveilling their Lie algebra content. (A.C.A.S.) [pt

  10. Noncommutative analysis, operator theory and applications

    CERN Document Server

    Cipriani, Fabio; Colombo, Fabrizio; Guido, Daniele; Sabadini, Irene; Sauvageot, Jean-Luc

    2016-01-01

    This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

  11. Stability analysis of black holes via a catastrophe theory and black hole thermodynamics in generalized theories of gravity

    International Nuclear Information System (INIS)

    Tamaki, Takashi; Torii, Takashi; Maeda, Kei-ichi

    2003-01-01

    We perform a linear perturbation analysis for black hole solutions with a 'massive' Yang-Mills field (the Proca field) in Brans-Dicke theory and find that the results are quite consistent with those via catastrophe theory where thermodynamic variables play an intrinsic role. Based on this observation, we show the general relation between these two methods in generalized theories of gravity which are conformally related to the Einstein-Hilbert action

  12. Naturalness in an Effective Field Theory for Neutron Star Matter

    International Nuclear Information System (INIS)

    Razeira, Moises; Vasconcellos, Cesar A.Z.; Bodmann, Bardo E.J.; Coelho, Helio T.; Dillig, Manfred

    2004-01-01

    High density hadronic matter is studied in a generalized relativistic multi-baryon lagrangian density. By comparing the predictions of our model with estimates obtained within a phenomenological naive dimensional analysis based on the naturalness of the coefficients of the theory, we show that naturalness plays a major role in effective field theory and, in combination with experiment, could represent a relevant criterium to select a model among others in the description of global static properties of neutron stars

  13. Butterfly tachyons in vacuum string field theory

    International Nuclear Information System (INIS)

    Matlock, Peter

    2003-01-01

    We use geometrical conformal field theory methods to investigate tachyon fluctuations about the butterfly projector state in vacuum string field theory. We find that the on-shell condition for the tachyon field is equivalent to the requirement that the quadratic term in the string-field action vanish on shell. This further motivates the interpretation of the butterfly state as a D-brane. We begin a calculation of the tension of the butterfly, and conjecture that this will match the case of the sliver and further strengthen this interpretation

  14. Stability in higher-derivative matter fields theories

    International Nuclear Information System (INIS)

    Tretyakov, Petr V.

    2016-01-01

    We discuss possible instabilities in higher-derivative matter field theories. These theories have two free parameters β 1 and β 4 . By using a dynamical system approach we explicitly demonstrate that for the stability of Minkowski space in an expanding universe we need the condition β 4 < 0. By using the quantum field theory approach we also find an additional restriction for the parameters, β 1 > -(1)/(3)β 4 , which is needed to avoid a tachyon-like instability. (orig.)

  15. Non-perturbative analysis of some simple field theories on a momentum space lattice

    International Nuclear Information System (INIS)

    Brooks, E.D. III.

    1984-01-01

    In this work, a new technique is developed for the numerical study of quantum field theory. The procedure, borrowed from nonrelativistic quantum mechanics, is that of finding the eigenvalues of a finite Hamiltonian matrix. The matrix is created by evaluating the matrix elements of the Hamiltonian operator on a finite basis of states. The eigenvalues and eigenvectors of the finite dimensional matrix become an accurate approximation to those of the physical system as the finite basis of states is extended to become more complete. A model of scalars coupled to fermions in 0 + 1 dimensions as a simple field theory is studied to consider in the course of developing the technique. Having developed the numerical and analytical techniques, a Fermi field coupled to a Bose field in 1 + 1 dimensions with the Yukawa coupling lambda anti-psi phi psi is considered. The large coupling limit basis of the 0 + 1 dimensional model is extended to this case using a Bogoliubov transformation on the fermions. It provides a handle on the behavior of the system in the large coupling limit. The effects of renormalization and the generation of bound states are considered

  16. Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory

    International Nuclear Information System (INIS)

    Moradpour, Hooman; Salako, Ines G.

    2016-01-01

    The restrictions on the Rastall theory due to application of the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy, and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.

  17. Non-local deformation of a supersymmetric field theory

    Energy Technology Data Exchange (ETDEWEB)

    Zhao, Qin [National University of Singapore, Department of Physics, Singapore (Singapore); Faizal, Mir [University of Lethbridge, Department of Physics and Astronomy, Lethbridge (Canada); University of British Columbia - Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); Shah, Mushtaq B.; Ganai, Prince A. [National Institute of Technology, Department of Physics, Srinagar, Kashmir (India); Bhat, Anha [National Institute of Technology, Department of Metallurgical and Materials Engineering, Srinagar (India); Zaz, Zaid [University of Kashmir, Department of Electronics and Communication Engineering, Srinagar, Kashmir (India); Masood, Syed; Raza, Jamil; Irfan, Raja Muhammad [International Islamic University, Department of Physics, Islamabad (Pakistan)

    2017-09-15

    In this paper, we will analyze a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative terms. In order to construct such a deformed N = 1 supersymmetric theory, a harmonic extension of functions will be used. However, the supersymmetry will only be preserved for a free theory and will be broken by the inclusion of interaction terms. (orig.)

  18. Effective field theory analysis on μ problem in low-scale gauge mediation

    International Nuclear Information System (INIS)

    Zheng Sibo

    2012-01-01

    Supersymmetric models based on the scenario of gauge mediation often suffer from the well-known μ problem. In this paper, we reconsider this problem in low-scale gauge mediation in terms of effective field theory analysis. In this paradigm, all high energy input soft mass can be expressed via loop expansions. If the corrections coming from messenger thresholds are small, as we assume in this letter, then all RG evaluations can be taken as linearly approximation for low-scale supersymmetric breaking. Due to these observations, the parameter space can be systematically classified and studied after constraints coming from electro-weak symmetry breaking are imposed. We find that some old proposals in the literature are reproduced, and two new classes are uncovered. We refer to a microscopic model, where the specific relations among coefficients in one of the new classes are well motivated. Also, we discuss some primary phenomenologies.

  19. The Supersymmetric Effective Field Theory of Inflation

    Energy Technology Data Exchange (ETDEWEB)

    Delacrétaz, Luca V.; Gorbenko, Victor [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94306 (United States); Senatore, Leonardo [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94306 (United States); Kavli Institute for Particle Astrophysics and Cosmology, Stanford University and SLAC,Menlo Park, CA 94025 (United States)

    2017-03-10

    We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable Stückelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplifying the analysis in this regime. We study the phenomenology of this Lagrangian. The Goldstino can have a non-relativistic dispersion relation. Gravitino and Goldstino affect the primordial curvature perturbations at loop level. The UV modes running in the loops generate three-point functions which are degenerate with the ones coming from operators already present in the absence of supersymmetry. Their size is potentially as large as corresponding to f{sub NL}{sup equil.,orthog.}∼1 or, for particular operators, even ≫1. The non-degenerate contribution from modes of order H is estimated to be very small.

  20. All the fundamental massless bosonic fields in superstring theory

    International Nuclear Information System (INIS)

    Manoukian, E.B.

    2012-01-01

    A systematic analysis of all the massless bosonic fields in superstring theory is carried out. Emphasis is put on the derivation of their propagators, their polarization aspects and the investigation of their underlying constraints as well as their number of degrees of freedom. The treatment is given in the presence of external sources, in the celebrated Coulomb gauge, ensuring the positivity of the formalism - a result which is also established in the process. The challenge here is the investigation involved in the self-dual fourth rank anti-symmetric tensor field. No constraints are imposed on the external sources so that their components may be varied independently, thus the complete expressions of the propagators may be obtained. As emphasized in our earlier work, the latter condition is an important one in dynamical theories with constraints giving rise to modifications as Faddeev-Popov factors. The analysis is carried out in 10 dimensions, not only because of the consistency requirement by the superstrings, but also in order to take into account of the self-duality character of the fourth rank anti-symmetric tensor field as spelled out in the paper. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  1. Introductory lectures on quantum field theory

    International Nuclear Information System (INIS)

    Alvarez-Gaume, L.; Vasquez-Mozo, M.A.

    2011-01-01

    In these lectures we present a few topics in quantum field theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to particle physics and string theory. (author)

  2. Aspects of renormalization in finite-density field theory

    Energy Technology Data Exchange (ETDEWEB)

    Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia

    2015-05-26

    We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

  3. Application of the weak-field asymptotic theory to the analysis of tunneling ionization of linear molecules

    DEFF Research Database (Denmark)

    Madsen, Lars Bojer; Tolstikhin, Oleg I.; Morishita, Toru

    2012-01-01

    The recently developed weak-field asymptotic theory [ Phys. Rev. A 84 053423 (2011)] is applied to the analysis of tunneling ionization of a molecular ion (H2+), several homonuclear (H2, N2, O2) and heteronuclear (CO, HF) diatomic molecules, and a linear triatomic molecule (CO2) in a static...... electric field. The dependence of the ionization rate on the angle between the molecular axis and the field is determined by a structure factor for the highest occupied molecular orbital. This factor is calculated using a virtually exact discrete variable representation wave function for H2+, very accurate...... Hartree-Fock wave functions for the diatomics, and a Hartree-Fock quantum chemistry wave function for CO2. The structure factors are expanded in terms of standard functions and the associated structure coefficients, allowing the determination of the ionization rate for any orientation of the molecule...

  4. Relating c 0 conformal field theories

    International Nuclear Information System (INIS)

    Guruswamy, S.; Ludwig, A.W.W.

    1998-03-01

    A 'canonical mapping' is established between the c = -1 system of bosonic ghosts at the c = 2 complex scalar theory and, a similar mapping between the c = -2 system of fermionic ghosts and the c = 1 Dirac theory. The existence of this mapping is suggested by the identity of the characters of the respective theories. The respective c 0 theories share the same space of states, whereas the spaces of conformal fields are different. Upon this mapping from their c 0) complex scalar and the Dirac theories inherit hidden nonlocal sl(2) symmetries. (author)

  5. Causality and superluminal behavior in classical field theories: Applications to k-essence theories and modified-Newtonian-dynamics-like theories of gravity

    International Nuclear Information System (INIS)

    Bruneton, Jean-Philippe

    2007-01-01

    Field theories with Lorentz (or diffeomorphism invariant) action can exhibit superluminal behavior through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagation is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories and stress the role played by the Cauchy problem and the notion of chronology. We show that, in general, superluminal behavior threatens causality only if one assumes that a prior chronology in spacetime exists. In the case where superluminal propagation occurs, however, there are at least two nonconformally related metrics in spacetime and thus two available notions of chronology. These two chronologies are on equal footing, and it would thus be misleading to choose ab initio one of them to define causality. Rather, we provide a formulation of causality in which no prior chronology is assumed. We argue that this is the only way to deal with the issue of causality in the case where some degrees of freedom propagate faster than others. In that framework, then, it is shown that superluminal propagation is not necessarily noncausal, the final answer depending on the existence of an initial data formulation. This also depends on global properties of spacetime that we discuss in detail. As an illustration of these conceptual issues, we consider two field theories, namely, k-essence scalar fields and bimetric theories of gravity, and we derive the conditions imposed by causality. We discuss various applications such as the dark energy problem, modified-Newtonian-dynamics-like theories of gravity, and varying speed of light theories

  6. Testing the master constraint programme for loop quantum gravity: V. Interacting field theories

    International Nuclear Information System (INIS)

    Dittrich, B; Thiemann, T

    2006-01-01

    This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein-Yang-Mills theory and 2 + 1 gravity. Interestingly, while Yang-Mills theory in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field theory on Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss constraint the master constraint can be solved explicitly, for the 2 + 1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by only using spectral methods is as complicated as for 3 + 1 gravity and we therefore leave the complete analysis for 3 + 1 gravity

  7. Little string theory from double-scaling limits of field theories

    International Nuclear Information System (INIS)

    Ling, Henry; Shieh, H.-H.; Anders, Greg van

    2007-01-01

    We show that little string theory on S 5 can be obtained as double-scaling limits of the maximally supersymmetric Yang-Mills theories on R x S 2 and R x S 3 /Z k . By matching the gauge theory parameters with those in the dual supergravity solutions found by Lin and Maldacena, we determine the limits in the gauge theories that correspond to decoupling of NS5-brane degrees of freedom. We find that for the theory on R x S 2 , the 't Hooft coupling must be scaled like ln 3 N, and on R x S 3 /Z k , like ln 2 N. Accordingly, taking these limits in these field theories gives Lagrangian definitions of little string theory on S 5

  8. Effective field theory: A modern approach to anomalous couplings

    International Nuclear Information System (INIS)

    Degrande, Céline; Greiner, Nicolas; Kilian, Wolfgang; Mattelaer, Olivier; Mebane, Harrison; Stelzer, Tim; Willenbrock, Scott; Zhang, Cen

    2013-01-01

    We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons. -- Highlights: •We discuss the advantages of effective field theories compared to anomalous couplings. •We show that one need not be concerned with unitarity violation at high energy. •We discuss the application of effective field theory to weak boson physics

  9. Holographic effective field theories

    Energy Technology Data Exchange (ETDEWEB)

    Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei' , Università di Padova,and INFN - Sezione di Padova, Via Marzolo 8, I-35131 Padova (Italy); Zaffaroni, Alberto [Dipartimento di Fisica, Università di Milano-Bicocca,and INFN - Sezione di Milano-Bicocca, I-20126 Milano (Italy)

    2016-06-28

    We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.

  10. Unambiguous formalism for higher order Lagrangian field theories

    International Nuclear Information System (INIS)

    Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn; Vankerschaver, Joris

    2009-01-01

    The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.

  11. Probabilistic theory of mean field games with applications

    CERN Document Server

    Carmona, René

    2018-01-01

    This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...

  12. Transversity results and computations in symplectic field theory

    Energy Technology Data Exchange (ETDEWEB)

    Fabert, Oliver

    2008-02-21

    Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M{sub {phi}} of symplectic manifolds (M,{omega}{sub M}) with symplectomorphisms {phi}. While the cylindrical contact homology of M{sub {phi}} is given by the Floer homologies of powers of {phi}, the other algebraic invariants of symplectic field theory for M{sub {phi}} provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian {phi} we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M{sub {phi}} {approx_equal} S{sup 1} x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic

  13. Lectures on classical and quantum theory of fields

    CERN Document Server

    Arodz, Henryk

    2017-01-01

    This textbook addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

  14. S-folds and 4d N=3 superconformal field theories

    Energy Technology Data Exchange (ETDEWEB)

    Aharony, Ofer [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 7610001 (Israel); Tachikawa, Yuji [Department of Physics, Faculty of Science,University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Kavli Institute for the Physics and Mathematics of the Universe,University of Tokyo, Kashiwa, Chiba 277-8583 (Japan)

    2016-06-08

    S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by García-Etxebarria and Regalado to provide the first construction of four dimensional N=3 superconformal theories. In this note, we classify the different variants of these N=3-preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the S-folds to three dimensional M-theory backgrounds. Upon adding D3-branes, these variants lead to different classes of N=3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography.

  15. Quantum golden field theory - Ten theorems and various conjectures

    International Nuclear Information System (INIS)

    El Naschie, M.S.

    2008-01-01

    Ten theorems and few conjectures related to quantum field theory as applied to high energy physics are presented. The work connects classical quantum field theory with the golden mean renormalization groups of non-linear dynamics and E-Infinity theory

  16. Developments in superstring field theory

    International Nuclear Information System (INIS)

    Green, M.B.

    1987-01-01

    In this article the structure of superstring theories is outlined. The one-loop quantum superstring gauge anomalies are then described and it is shown that their absence leads to an interesting theory with gauge group SO(32). The one-loop infinities also cancel for this gauge group. The anomaly cancellation can be understood in terms of the low-energy effective supergravity-Yang-Mills field theory, from which it is shown that E 8 x E 8 is an equally good gauge group, which suggests that there should also be an interesting E 8 x E 8 superstring theory. A new type of superstring theory, known as the 'heterotic' string theory, which only describes strings with gauge groups E 8 x E 8 or SO(32) is described. Finally some very exciting prospects for obtaining a sensible description of four-dimensional physics from a ten-dimensional superstring theory with gauge group E 8 x E 8 is outlined. (author)

  17. Variational methods for field theories

    Energy Technology Data Exchange (ETDEWEB)

    Ben-Menahem, S.

    1986-09-01

    Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.

  18. Generalized field theory of gravitation

    International Nuclear Information System (INIS)

    Yilmaz, H.

    1976-01-01

    It is shown that if, on empirical grounds, one rules out the existence of cosmic fields of Dicke-Brans (scalar) and Will Nordvedt (vector, tensor) type, then the most general experimentally viable and theoretically reasonable theory of gravitation seems to be a LAMBDA-dependent generalization of Einstein and Yilmez theories, which reduces to the former for LAMBDA=0 and to the latter for LAMBDA=1

  19. Random walks, critical phenomena, and triviality in quantum field theory

    International Nuclear Information System (INIS)

    Fernandez, R.; Froehlich, J.; Sokal, A.D.

    1992-01-01

    The subject of this book is equilibrium statistical mechanics - in particular the theory of critical phenomena - and quantum field theory. A general review of the theory of critical phenomena in spin systems, field theories, and random-walk and random-surface models is presented. Among the more technical topics treated in this book, the central theme is the use of random-walk representations as a tool to derive correlation inequalities. The consequences of these inequalities for critical-exponent theory and the triviality question in quantum field theory are expounded in detail. The book contains some previously unpublished results. It addresses both the researcher and the graduate student in modern statistical mechanics and quantum field theory. (orig.)

  20. Unified field theory on the basis of the projective theory of relativity

    International Nuclear Information System (INIS)

    Lessner, G.

    1982-01-01

    A unified field theory is developed on the basis of the five-dimensional vacuum equations R/sub munu/ = 0 in the projective theory of relativity. The four-dimensional field equations following from R/sub munu/ = 0 by projection are a generalized Einstein-Maxwell theory, for which the generalization is given by a scalar field. The particle concept based on these equations represents the intrinsic particle properties, which are the rest mass, or the energy in case of photons and neutrinos, the charge and the spin by integrals of the field distribution extended over spacelike hypersurfaces. The energy concept is based on Moller's energy-momentum complex. Moller's argument against his energy-momentum complex is discussed and refuted. The spin concept is derived from the axial symmetry of the field distribution. The stationary axially symmetric field is studied in detail. In the spherically symmetric static case the solutions of the field equations are given and investigated for their particle properties. It is shown that one and only one type of solution yields a good approach to the distribution of charge and rest mass in the proton. However, none of the spherically symmetric solutions represents the electron

  1. Holographic applications of logarithmic conformal field theories

    NARCIS (Netherlands)

    Grumiller, D.; Riedler, W.; Rosseel, J.; Zojer, T.

    2013-01-01

    We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in anti-de Sitter space and logarithmic conformal field theories in

  2. Logarithmic conformal field theory

    Science.gov (United States)

    Gainutdinov, Azat; Ridout, David; Runkel, Ingo

    2013-12-01

    Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more

  3. Unified-field theory: yesterday, today, tomorrow

    International Nuclear Information System (INIS)

    Bergman, P.G.

    1982-01-01

    Beginning with the expounding of Einstein understanding of advantages and disadvantages of general relativity theory, the authors proceed to consideration of what the complete unified theory have to be according to Einstein. The four theories which can be considered as ''unified'', namely weyl and Calutsa ones, worked out a half of century ago, and twistor twisting and supersymmetry theories, nowadays attracting attention, are briefly described and discussed. The authors come to a conclusion that achievements in elementary-particle physics have to affect any future theory, that this theory has to explain the principle contradictions between classical and quantum field theories, and that finally it can lead to change of the modern space-time model as a four-dimensional variety

  4. Supersymmetrical dual string theories and their field theory limits: A review

    International Nuclear Information System (INIS)

    Green, M.B.

    1985-01-01

    This paper outlines the construction and properties of supersymmetric string theories. Such theories, which describe the quantum mechanics of relativistic strings in ten-space time dimensions contain both N=4 Yang-Mills and N=8 supergravity field theories as special limits in which the string tension becomes infinite. Calculations of one-loop S-matrix elements reveal remarkable finiteness properties

  5. Quantum field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Jegerlehner, F.

    1975-01-01

    At first a heuristic understanding is given how the relation between quantum field theory and statistical mechanics near phase transitions comes about. A long range scale invariant theory is constructed, critical indices are calculated and the relations among them are proved, field theoretical Kadanoff-scale transformations are formulated and scaling corrections calculated. A precise meaning to many of Kadanoffs considerations and a model matching Wegners phenomenological scheme is given. It is shown, that soft parametrization is most transparent for the discussion of scaling behaviour. (BJ) [de

  6. Dual field theory of strong interactions

    International Nuclear Information System (INIS)

    Akers, D.

    1987-01-01

    A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant α = 1/137

  7. Infrared and ultraviolet behaviour of effective scalar field theory

    International Nuclear Information System (INIS)

    Ball, R.D.; Thorne, R.S.

    1995-01-01

    We consider the infrared and ultraviolet behaviour of the effective quantum field theory of a single Z 2 symmetric scalar field. In a previous paper we proved to all orders in perturbation theory the renormalizability of massive effective scalar field theory using Wilson's exact renormalization group equation. Here we show that away from exceptional momenta the massless theory is similarly renormalizable, and we prove detailed bounds on Green's functions as arbitrary combinations of exceptional Euclidean momenta are approached. As a corollary we also Weinberg's Theorem for the massive effective theory, n the form of bounds on Green's functions at Euclidean momenta much greater than the particle mass but below the naturalness scale of theory. 12 refs

  8. Infrared and ultraviolet behaviour of effective scalar field theory

    CERN Document Server

    Ball, R D

    1995-01-01

    We consider the infrared and ultraviolet behaviour of the effective quantum field theory of a single Z_2 symmetric scalar field. In a previous paper we proved to all orders in perturbation theory the renormalizability of massive effective scalar field theory using Wilson's exact renormalization group equation. Here we show that away from exceptional momenta the massless theory is similarly renormalizable, and we prove detailed bounds on Green's functions as arbitrary combinations of exceptional Euclidean momenta are approached. As a corollary we also prove Weinberg's Theorem for the massive effective theory, in the form of bounds on Green's functions at Euclidean momenta much greater than the particle mass but below the naturalness scale of the theory.

  9. Statistical approach to quantum field theory. An introduction

    International Nuclear Information System (INIS)

    Wipf, Andreas

    2013-01-01

    Based on course-tested notes and pedagogical in style. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Contains end-of-chapter problems and listings of short, useful computer programs. Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an ''experimental'' tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as

  10. A general field-covariant formulation of quantum field theory

    International Nuclear Information System (INIS)

    Anselmi, Damiano

    2013-01-01

    In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because of this, we cannot write simple identities relating bare and renormalized generating functionals, or generating functionals before and after nonlinear changes of field variables. In this paper we investigate this issue and work out a general field-covariant approach to quantum field theory, which allows us to treat all perturbative changes of field variables, including the relation between bare and renormalized fields, as true changes of variables in the functional integral, under which the functionals Z and W=lnZ behave as scalars. We investigate the relation between composite fields and changes of field variables, and we show that, if J are the sources coupled to the elementary fields, all changes of field variables can be expressed as J-dependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variable-changes and the renormalization of composite fields. Using our transformation rules it is possible to derive the renormalization of a theory in a new variable frame from the renormalization in the old variable frame, without having to calculate it anew. We define several approaches, useful for different purposes, in particular a linear approach where all variable changes are described as linear source redefinitions. We include a number of explicit examples. (orig.)

  11. Relating the archetypes of logarithmic conformal field theory

    International Nuclear Information System (INIS)

    Creutzig, Thomas; Ridout, David

    2013-01-01

    Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal. These include the c=−2 triplet model, the Wess–Zumino–Witten model on SL(2;R) at level k=−1/2 , and its supergroup analogue on GL(1|1). Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras. The results show that the archetypes of logarithmic conformal field theory are in fact all very closely related, as are many other examples including, in particular, the SL(2|1) models at levels 1 and −1/2 . The conclusion is then that the archetypal examples of logarithmic conformal field theory are practically all the same, so we should not expect that their features are in any way generic. Further archetypal examples must be sought

  12. Relating the archetypes of logarithmic conformal field theory

    Energy Technology Data Exchange (ETDEWEB)

    Creutzig, Thomas, E-mail: tcreutzig@mathematik.tu-darmstadt.de [Department of Physics and Astronomy, University of North Carolina, Phillips Hall, CB 3255, Chapel Hill, NC 27599-3255 (United States); Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt (Germany); Ridout, David, E-mail: david.ridout@anu.edu.au [Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200 (Australia)

    2013-07-21

    Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal. These include the c=−2 triplet model, the Wess–Zumino–Witten model on SL(2;R) at level k=−1/2 , and its supergroup analogue on GL(1|1). Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras. The results show that the archetypes of logarithmic conformal field theory are in fact all very closely related, as are many other examples including, in particular, the SL(2|1) models at levels 1 and −1/2 . The conclusion is then that the archetypal examples of logarithmic conformal field theory are practically all the same, so we should not expect that their features are in any way generic. Further archetypal examples must be sought.

  13. Informal meeting on recent developments in field theory

    International Nuclear Information System (INIS)

    Anon.

    1977-12-01

    A topical meeting on recent developments in field theory was organized by the International Centre for Theoretical Physics from 21 to 23 November 1977. The publication is a compilation of the abstracts of lecture given. The mayor themes of the meeting were the problem of confinement, the quantization of Yang-Mills theories and the topological aspects of field theories in flat and curved spaces

  14. Quantum theory of noncommutative fields

    International Nuclear Information System (INIS)

    Carmona, J.M.; Cortes, J.L.; Gamboa, J.; Mendez, F.

    2003-01-01

    Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of 'noncommutative fields'. Our description permits to break the usual particle-antiparticle degeneracy at the dispersion relation level and introduces naturally an ultraviolet and an infrared cutoff. Phenomenological bounds for these new energy scales are given. (author)

  15. Orbital effect of the magnetic field in dynamical mean-field theory

    Science.gov (United States)

    Acheche, S.; Arsenault, L.-F.; Tremblay, A.-M. S.

    2017-12-01

    The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate, and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.

  16. Convergent perturbation expansions for Euclidean quantum field theory

    International Nuclear Information System (INIS)

    Mack, G.; Pordt, A.

    1984-09-01

    Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean Quantum Field Theory to arbitrary accuracy, including 'nonperturbative' contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional lambdaphi 4 -theory (in continuous space). They are not essentially more complicated than standard perturbation theory. The n-th order term is expressed in terms of 0(n)-dimensional integrals, and is of order lambda 4 if 4k-3<=n<=4k. (orig.)

  17. Constraints on Interacting Scalars in 2T Field Theory and No Scale Models in 1T Field Theory

    CERN Document Server

    Bars, Itzhak

    2010-01-01

    In this paper I determine the general form of the physical and mathematical restrictions that arise on the interactions of gravity and scalar fields in the 2T field theory setting, in d+2 dimensions, as well as in the emerging shadows in d dimensions. These constraints on scalar fields follow from an underlying Sp(2,R) gauge symmetry in phase space. Determining these general constraints provides a basis for the construction of 2T supergravity, as well as physical applications in 1T-field theory, that are discussed briefly here, and more detail elsewhere. In particular, no scale models that lead to a vanishing cosmological constant at the classical level emerge naturally in this setting.

  18. [Topics in field theory and string theory

    International Nuclear Information System (INIS)

    1990-01-01

    In the past year, I have continued to investigate the relations between conformal field theories and lattice statistical mechanical models, and in particular have been studying two dimensional models coupled to quantum gravity. I have continued as well to consider possible extension of these results to higher dimensions and potential applications in other contexts

  19. Twisted conformal field theories and Morita equivalence

    Energy Technology Data Exchange (ETDEWEB)

    Marotta, Vincenzo [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' and INFN, Sezione di Napoli, Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy); Naddeo, Adele [CNISM, Unita di Ricerca di Salerno and Dipartimento di Fisica ' E.R. Caianiello' , Universita degli Studi di Salerno, Via Salvador Allende, 84081 Baronissi (Italy); Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy)], E-mail: adelenaddeo@yahoo.it

    2009-04-01

    The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter {theta} (in appropriate units): an isomorphism is established between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space. We focus on a particular conformal field theory (CFT), the one obtained by means of the m-reduction procedure [V. Marotta, J. Phys. A 26 (1993) 3481; V. Marotta, Mod. Phys. Lett. A 13 (1998) 853; V. Marotta, Nucl. Phys. B 527 (1998) 717; V. Marotta, A. Sciarrino, Mod. Phys. Lett. A 13 (1998) 2863], and show that it is the Morita equivalent of a NCFT. Finally, the whole m-reduction procedure is shown to be the image in the ordinary space of the Morita duality. An application to the physics of a quantum Hall fluid at Jain fillings {nu}=m/(2pm+1) is explicitly discussed in order to further elucidate such a correspondence and to clarify its role in the physics of strongly correlated systems. A new picture emerges, which is very different from the existing relationships between noncommutativity and many body systems [A.P. Polychronakos, arXiv: 0706.1095].

  20. Lectures on interacting string field theory

    International Nuclear Information System (INIS)

    Jevicki, A.

    1986-09-01

    We give a detailed review of the current formulations of interacting string field theory. The historical development of the subject is taken beginning with the old dual resonance model theory. The light cone approach is reviewed in some detail with emphasis on conformal mapping techniques. Witten's covariant approach is presented. The main body of the lectures concentrates on developing the operator formulation of Witten's theory. 38 refs., 22 figs., 5 tabs

  1. A computational theory of visual receptive fields.

    Science.gov (United States)

    Lindeberg, Tony

    2013-12-01

    A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative

  2. N=8 supersingleton quantum field theory

    International Nuclear Information System (INIS)

    Bergshoeff, E.; Salam, A.; Sezgin, E.; Tanii, Yoshiaki.

    1988-06-01

    We quantise the N=8 supersymmetric singleton field theory which is formulated on the boundary of the four dimensional anti de Sitter spacetime (AdS 4 ). The theory has rigid OSp(8,4) symmetry which acts as a superconformal group on the boundary of AdS 4 . We show that the generators of this symmetry satisfy the full quantum OSp(8,4) algebra. The spectrum of the theory contains massless states of all higher integer and half-integer spin which fill the irreducible representations of OSp(8,4) with highest spin s max =2,4,6,... Remarkably, these are in one to one correspondence with the generators of Vasiliev's infinite dimensional extended higher spin superalgebra shs(8,4), suggesting that we may have stumbled onto a field theoretic realization of this algebra. We also discuss the possibility of a connection between the N=8 supersingleton theory with the eleven dimensional supermembrane in an AdS 4 xS 7 background. (author). 34 refs

  3. Field theory a path integral approach

    CERN Document Server

    Das, Ashok

    2006-01-01

    This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.

  4. Quantum field theory

    International Nuclear Information System (INIS)

    Mancini, F.

    1986-01-01

    Theoretical physicists, coming from different countries, working on different areas, gathered at Positano: the Proceedings contain all the lectures delivered as well as contributed papers. Many areas of physics are represented, elementary particles in high energy physics, quantum relativity, quantum geometry, condensed matter physics, statistical mechanics; but all works are concerned with the use of the methods of quantum field theory. The first motivation of the meeting was to pay homage to a great physicist and a great friend; it was also an occasion in which theoretical physicists got together to discuss and to compare results in different fields. The meeting was very intimate; the relaxed atmosphere allowed constructive discussions and contributed to a positive exchange of ideas. (orig.)

  5. Constraints on four dimensional effective field theories from string and F-theory

    Energy Technology Data Exchange (ETDEWEB)

    Baume, Florent

    2017-06-21

    This thesis is a study of string theory compactifications to four dimensions and the constraints the Effective Field theories must exhibit, exploring both the closed and open sectors. In the former case, we focus on axion monodromy scenarios and the impact the backreaction of the energy density induced by the vev of an axion has on its field excursions. For all the cases studied, we find that the backreaction is small up to a critical value, and the proper field distance is flux independent and at most logarithmic in the axion vev. We then move to the open sector, where we use the framework of F-theory. We first explore the relation between the spectra arising from F-theory GUTs and those coming from a decomposition of the adjoint of E{sub 8} to SU(5) x U(1){sup n}. We find that extending the latter spectrum with new SU(5)-singlet fields, and classifying all possible ways of breaking the Abelian factors, all the spectra coming from smooth elliptic fibration constructed in the literature fit in our classification. We then explore generic properties of the spectra arising when breaking SU(5) to the Standard Model gauge group while retaining some anomaly properties. We finish by a study of F-theory compactications on a singular elliptic fibration via Matrix Factorisation, and find the charged spectrum of two non-Abelian examples.

  6. Constraints on four dimensional effective field theories from string and F-theory

    International Nuclear Information System (INIS)

    Baume, Florent

    2017-01-01

    This thesis is a study of string theory compactifications to four dimensions and the constraints the Effective Field theories must exhibit, exploring both the closed and open sectors. In the former case, we focus on axion monodromy scenarios and the impact the backreaction of the energy density induced by the vev of an axion has on its field excursions. For all the cases studied, we find that the backreaction is small up to a critical value, and the proper field distance is flux independent and at most logarithmic in the axion vev. We then move to the open sector, where we use the framework of F-theory. We first explore the relation between the spectra arising from F-theory GUTs and those coming from a decomposition of the adjoint of E 8 to SU(5) x U(1) n . We find that extending the latter spectrum with new SU(5)-singlet fields, and classifying all possible ways of breaking the Abelian factors, all the spectra coming from smooth elliptic fibration constructed in the literature fit in our classification. We then explore generic properties of the spectra arising when breaking SU(5) to the Standard Model gauge group while retaining some anomaly properties. We finish by a study of F-theory compactications on a singular elliptic fibration via Matrix Factorisation, and find the charged spectrum of two non-Abelian examples.

  7. Topics in conformal field theory

    International Nuclear Information System (INIS)

    Kiritsis, E.B.

    1988-01-01

    In this work two major topics in Conformal Field Theory are discussed. First a detailed investigation of N = 2 Superconformal theories is presented. The structure of the representations of the N = 2 superconformal algebras is investigated and the character formulae are calculated. The general structure of N = 2 superconformal theories is elucidated and the operator algebra of the minimal models is derived. The first minimal system is discussed in more detail. Second, applications of the conformal techniques are studied in the Ashkin-Teller model. The c = 1 as well as the c = 1/2 critical lines are discussed in detail

  8. Massive deformations of Type IIA theory within double field theory

    Science.gov (United States)

    Çatal-Özer, Aybike

    2018-02-01

    We obtain massive deformations of Type IIA supergravity theory through duality twisted reductions of Double Field Theory (DFT) of massless Type II strings. The mass deformation is induced through the reduction of the DFT of the RR sector. Such reductions are determined by a twist element belonging to Spin+(10, 10), which is the duality group of the DFT of the RR sector. We determine the form of the twists and give particular examples of twists matrices, for which a massive deformation of Type IIA theory can be obtained. In one of the cases, requirement of gauge invariance of the RR sector implies that the dilaton field must pick up a linear dependence on one of the dual coordinates. In another case, the choice of the twist matrix violates the weak and the strong constraints explicitly in the internal doubled space.

  9. Integrable structures in quantum field theory

    International Nuclear Information System (INIS)

    Negro, Stefano

    2016-01-01

    This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q -operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only. (topical review)

  10. Vergnaud s Theory of Conceptual Fields as a tool for the didactic planning

    Directory of Open Access Journals (Sweden)

    Gabriel Dias de Carvalho Júnior

    2008-08-01

    Full Text Available The aim of this work is to present Vergnaud s Theory of Conceptual Fields (1990 as a tool for the design and analysis of Science teaching sequences. The classroom study was conducted in a Brazilian High School working with Thermal Physics. It was part of a Master Degree Thesis presented by one of the authors (CARVALHO JR., 2005, in which we followed up the learning pathways of 7 students. The results of this study were analyzed using the Theory of Conceptual Fields. We shall emphasize the main concepts and categories of Vergnaud s Theory and the appropriation we have done about them in this particular research.

  11. Infinitely many inequivalent field theories from one Lagrangian

    CERN Document Server

    100__; Mavromatos, Nick E.; Sarkar, Sarben

    2014-01-01

    Logarithmic time-like Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field $\\phi$. In Euclidean space the Lagrangian of such a theory, $L=\\frac{1}{2}(\

  12. Les Houches lectures on large N field theories and gravity

    International Nuclear Information System (INIS)

    Maldacena, J.

    2002-01-01

    We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions. (authors)

  13. Perturbative algebraic quantum field theory an introduction for mathematicians

    CERN Document Server

    Rejzner, Kasia

    2016-01-01

    Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are th...

  14. Effective field theory for triaxially deformed nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Q.B. [Technische Universitaet Muechen, Physik-Department, Garching (Germany); Peking University, State Key Laboratory of Nuclear Physics and Technology, School of Physics, Beijing (China); Kaiser, N. [Technische Universitaet Muechen, Physik-Department, Garching (Germany); Meissner, Ulf G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Institute for Advanced Simulation, Institut fuer Kernphysik, Juelich Center for Hadron Physics and JARA-HPC, Forschungszentrum Juelich, Juelich (Germany); Meng, J. [Peking University, State Key Laboratory of Nuclear Physics and Technology, School of Physics, Beijing (China); Beihang University, School of Physics and Nuclear Energy Engineering, Beijing (China); University of Stellenbosch, Department of Physics, Stellenbosch (South Africa)

    2017-10-15

    Effective field theory is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. The Hamiltonian for the triaxial rotor is obtained up to next-to-leading order within the effective field theory formalism. Its applicability is examined by comparing with a five-dimensional rotor-vibrator Hamiltonian for the description of the energy spectra of the ground state and γ band in Ru isotopes. It is found that by taking into account the next-to-leading order corrections, the ground state band in the whole spin region and the γ band in the low spin region are well described. The deviations for high-spin states in the γ bands point towards the importance of including vibrational degrees of freedom in the effective field theory formulation. (orig.)

  15. Electromagnetic Field Theory A Collection of Problems

    CERN Document Server

    Mrozynski, Gerd

    2013-01-01

    After a brief introduction into the theory of electromagnetic fields and the definition of the field quantities the book teaches the analytical solution methods of Maxwell’s equations by means of several characteristic examples. The focus is on static and stationary electric and magnetic fields, quasi stationary fields, and electromagnetic waves. For a deeper understanding, the many depicted field patterns are very helpful. The book offers a collection of problems and solutions which enable the reader to understand and to apply Maxwell’s theory for a broad class of problems including classical static problems right up to waveguide eigenvalue problems. Content Maxwell’s Equations - Electrostatic Fields - Stationary Current Distributions – Magnetic Field of Stationary Currents – Quasi Stationary Fields: Eddy Currents - Electromagnetic Waves Target Groups Advanced Graduate Students in Electrical Engineering, Physics, and related Courses Engineers and Physicists Authors Professor Dr.-Ing. Gerd Mrozynski...

  16. Density dependent hadron field theory

    International Nuclear Information System (INIS)

    Fuchs, C.; Lenske, H.; Wolter, H.H.

    1995-01-01

    A fully covariant approach to a density dependent hadron field theory is presented. The relation between in-medium NN interactions and field-theoretical meson-nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson-nucleon vertices on the baryon field operators. As a consequence, the Euler-Lagrange equations lead to baryon rearrangement self-energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy-momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean-field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac-Brueckner calculations with the Bonn NN potentials are used. Results from Hartree calculations for energy spectra, binding energies, and charge density distributions of 16 O, 40,48 Ca, and 208 Pb are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultaneous improvement of charge radii, charge densities, and binding energies. The results indicate the appearance of a new ''Coester line'' in the nuclear matter equation of state

  17. From topological quantum field theories to supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Bossard, G.

    2007-10-01

    This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the β function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)

  18. Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories arXiv

    CERN Document Server

    Alexandre, Jean; Millington, Peter; Seynaeve, Dries

    We demonstrate the extension to PT-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimisation of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantisation of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.

  19. Towards quantum gravity via quantum field theory. Problems and perspectives

    Energy Technology Data Exchange (ETDEWEB)

    Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)

    2016-07-01

    General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.

  20. Open and Closed String field theory interpreted in classical Algebraic Topology

    OpenAIRE

    Sullivan, Dennis

    2003-01-01

    There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.

  1. Recent progress in reggeon field theory

    International Nuclear Information System (INIS)

    Sugar, R.L.

    1977-01-01

    The present status of the pomeron theory in the reggeon field theory is summarized. For α 0 ( 0 -a bare intercept, αsub(oc) - a certain critical value) the theory is in a very good shape. It appears to satisfy both S and t-channel unitarity, and to avoid all of the decreases which plagued the simple pole model of the pomeron. For α 0 >αsub(oc) the situation is less clear

  2. Quantum field theory a tourist guide for mathematicians

    CERN Document Server

    Folland, Gerald B

    2008-01-01

    Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theor...

  3. Cosmological field theory for observational astronomers

    International Nuclear Information System (INIS)

    Zel'Dovich, Y.B.

    1987-01-01

    Theories of the very early Universe that use scalar fields (i.e., the so-called inflationary models of the Universe) have now come into wide use. The inflationary universe approach may perhaps solve some of the most difficult enigmas about the Universe as a whole. The inflationary universe forms a good bridge between the quantum theory of the birth of the Universe (which is still in the initial stages of development) and the standard hot Big Bang theory (which is well established, at least qualitatively). Therefore, an understanding of the basic ideas of inflation is a must for astronomers interested in the broad picture of the science. Astronomers are mathematically oriented enough (via celestial mechanics, electromagnetic theory, magnetohydrodynamics, nuclear reactions,etc.) that there is no negative attitude towards formulae in general. What the astronomer lacks is a knowledge of recent developments in particle physics and field theory. The astronomer should not be blamed for this, because these branches of physics are developing in a very peculiar fashion: some subfields of it are progressing comparatively slowly, with experimental verifications at each and every step, while other subfields progress rapidly

  4. A Chern-Simons-like action for closed-string field theory

    International Nuclear Information System (INIS)

    Taylor, C.C.

    1989-01-01

    A Chern-Simons-like action is proposed for closed-string field theory. The action involves auxiliary fields of arbitrary ghost number and is defined in terms of the closed-string operations ∫, Q and *, analogous to those introduced by Witten in the construction of open-string field theory. The action is an extension of one proposed for free closed strings and bears a formal relationship to 2 + 1 gravity analogous to that between open-string field theory and (2 + 1)-dimensional Yang-Mills theory. (author)

  5. Superstring field theory

    International Nuclear Information System (INIS)

    Green, M.B.

    1984-01-01

    Superstring field theories are formulated in terms of light-cone-gauge superfields that are functionals of string coordinates chi(sigma) and theta(sigma). The formalism used preserves only the manifest SU(4) symmetry that corresponds to rotations among six of the eight transverse directions. In type I theories, which have one ten-dimensional supersymmetry and describe both open and closed strings, there are five interaction terms of two basic kinds. One kind is a breaking or joining interaction, which is a string generalization of a cubic Yang-Mills coupling. It is relevant to both the three open-string vertex and the open-string to closed-string transition vertex. The other kind is an exchange or crossing-over interaction, which is a string generalization of a cubic gravitational coupling. All the interactions can be uniquely determined by requiring continuity of the coordinates chi(sigma) and theta(sigma) (which implies local conservation of the conjugate momenta) and by imposing the global supersymmetry algebra. Specific local operators are identified for each of the two kinds of interactions. In type II theories, which have two ten-dimensional supersymmetries and contain closed strings only, the entire interaction hamiltonian consists of a single cubic vertex. The higher-order contact terms of the N=8 supergravity theory that arises in the low-energy limit give an effective description of the exchange of massive string modes. (orig.)

  6. Energy momentum tensor and marginal deformations in open string field theory

    International Nuclear Information System (INIS)

    Sen, Ashoke

    2004-01-01

    Marginal boundary deformations in a two dimensional conformal field theory correspond to a family of classical solutions of the equations of motion of open string field theory. In this paper we develop a systematic method for relating the parameter labelling the marginal boundary deformation in the conformal field theory to the parameter labelling the classical solution in open string field theory. This is done by first constructing the energy-momentum tensor associated with the classical solution in open string field theory using Noether method, and then comparing this to the answer obtained in the conformal field theory by analysing the boundary state. We also use this method to demonstrate that in open string field theory the tachyon lump solution on a circle of radius larger than one has vanishing pressure along the circle direction, as is expected for a co-dimension one D-brane. (author)

  7. Effective Field Theories and the Role of Consistency in Theory Choice

    CERN Document Server

    Wells, James D

    2012-01-01

    Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the importance of these attributes pales in comparison with consistency, both observational and mathematical consistency, which propels the effective theory to be superior to its simpler truncated version of finite terms, whether that theory be renormalizable (e.g., Standard Model of particle physics) or nonrenormalizable (e.g., gravity). Some implications for the Large Hadron Collider and beyond are discussed, including comments on how directly acknowledging the preeminence of consistency can affect future theory work.

  8. Effective field theories for correlated electrons

    International Nuclear Information System (INIS)

    Wallington, J.P.

    1999-10-01

    In this thesis, techniques of functional integration are applied to the construction of effective field theories for models of strongly correlated electrons. This is accomplished by means of the Hubbard-Stratonovic transformation which maps a system of interacting fermions onto one of free fermions interacting, not with each other, but with bosonic fields representing the collective modes of the system. Different choices of transformation are investigated throughout the thesis. It is shown that there exists a new group of discrete symmetries and transformations of the Hubbard model. Using this new group, the problem of choosing a Hubbard-Stratonovic decomposition of the Hubbard interaction term is solved. In the context of the exotic doped barium bismuthates, an extended Hubbard model with on-site attraction and nearest neighbour repulsion is studied. Mean field and renormalisation group analyses show a 'pseudospin-flop' from charge density wave to superconductivity as a function of filling. The nearest neighbour attractive Hubbard model on a quasi-2D lattice is studied as a simple phenomenological model for the high-T c cuprates. Mean field theory shows a transition from pure d-wave to pure s-wave superconductivity, via a mixed symmetry s + id state. Using Gaussian fluctuations, the BCS-Bose crossover is examined and suggestions are made about the origin of the angle dependence of the pseudogap. The continuum delta-shell potential model is introduced for anisotropic superconductors. Its mean field phases are studied and found to have some unusual properties. The BCS-Bose crossover is examined and the results are compared with those of the lattice model. Quasi-2D (highly anisotropic 3D) systems are considered. The critical properties of a Bose gas are investigated as the degree of anisotropy is varied. A new 2D Bose condensate state is found. A renormalisation group analysis is used to investigate the crossover from 2D to 3D. (author)

  9. Note on Weyl versus conformal invariance in field theory

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Feng [Nanchang University, Department of Physics, Nanchang (China)

    2017-12-15

    It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that generically unitarity alone is not sufficient for a conformal field theory to be Weyl invariant. Furthermore, we show explicitly that when a unitary conformal field theory couples to gravity in a Weyl-invariant way, each primary scalar operator that is either relevant or marginal in the unitary conformal field theory corresponds to a Weyl-covariant operator in the curved background. (orig.)

  10. Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.

    Energy Technology Data Exchange (ETDEWEB)

    Scheck, Florian

    2018-04-01

    Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.

  11. Structural aspects of quantum field theory and noncommutative geometry

    CERN Document Server

    Grensing, Gerhard

    2013-01-01

    This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...

  12. On the scaling limits in the Euclidean (quantum) field theory

    International Nuclear Information System (INIS)

    Gielerak, R.

    1983-01-01

    The author studies the concept of scaling limits in the context of the constructive field theory. He finds that the domain of attraction of a free massless Euclidean scalar field in the two-dimensional space time contains almost all Euclidean self-interacting models of quantum fields so far constructed. The renormalized scaling limit of the Wick polynomials of several self-interacting Euclidean field theory models are shown to be the same as in the free field theory. (Auth.)

  13. Light front field theory: an advanced primer

    International Nuclear Information System (INIS)

    Martinovic, L.

    2007-01-01

    We present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two/dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a 'light-like' limit of the usual field theory quantized on a initial space-like surface. A simple LF formulation of the Higgs mechanism is then given Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and number of technical details and derivations are contained in the appendices (Author)

  14. Axiomatic Quantum Field Theory in Terms of Operator Product Expansions: General Framework, and Perturbation Theory via Hochschild Cohomology

    Directory of Open Access Journals (Sweden)

    Stefan Hollands

    2009-09-01

    Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.

  15. Toward a gauge field theory of gravity.

    Science.gov (United States)

    Yilmaz, H.

    Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.

  16. Scaling algebras and renormalization group in algebraic quantum field theory

    International Nuclear Information System (INIS)

    Buchholz, D.; Verch, R.

    1995-01-01

    For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)

  17. Minimal flavour violation an effective field theory approach

    CERN Document Server

    D'Ambrosio, G.; Isidori, G.; Strumia, A.

    2002-01-01

    We present a general analysis of extensions of the Standard Model which satisfy the criterion of Minimal Flavour Violation (MFV). We define this general framework by constructing a low-energy effective theory containing the Standard Model fields, with one or two Higgs doublets and, as the only source of SU(3)^5 flavour symmetry breaking, the background values of fields transforming under the flavour group as the ordinary Yukawa couplings. We analyse present bounds on the effective scale of dimension-six operators, which range between 1 and 10 TeV, with the most stringent constraints imposed by B -> X_s gamma. In this class of theories, it is possible to relate predictions for FCNC processes in B physics to those in K physics. We compare the sensitivity of various experimental searches in probing the hypothesis of MFV. Within the two-Higgs-doublet scenario, we develop a general procedure to obtain all tan(beta)-enhanced Higgs-mediated FCNC amplitudes, discussing in particular their impact in B -> l^+l^-, Delta...

  18. Boundary states in c=-2 logarithmic conformal field theory

    International Nuclear Information System (INIS)

    Bredthauer, Andreas; Flohr, Michael

    2002-01-01

    Starting from first principles, a constructive method is presented to obtain boundary states in conformal field theory. It is demonstrated that this method is well suited to compute the boundary states of logarithmic conformal field theories. By studying the logarithmic conformal field theory with central charge c=-2 in detail, we show that our method leads to consistent results. In particular, it allows to define boundary states corresponding to both, indecomposable representations as well as their irreducible subrepresentations

  19. Conformal field theory and its application to strings

    International Nuclear Information System (INIS)

    Verlinde, E.P.

    1988-01-01

    Conformal field theories on Riemann surfaces are considered and the result is applied to study the loop amplitudes for bosonic strings. It is shown that there is a close resemblance between the loop amplitudes for φ 3 -theory and the expressions for string multi-loop amplitudes. The similarity between φ 3 -amplitudes in curved backgrounds and the analytic structure of string amplitudes in backgrounds described by conformal field theories is also pointed out. 60 refs.; 5 figs.; 200 schemes

  20. On the construction of classical superstring field theories

    Energy Technology Data Exchange (ETDEWEB)

    Konopka, Sebastian Johann Hermann

    2016-07-01

    This thesis describes the construction of classical superstring field theories based on the small Hilbert space. First we describe the traditional construction of perturbative superstring theory as an integral over the supermoduli space of type II world sheets. The geometry of supermoduli space dictates many algebraic properties of the string field theory action. In particular it allows for an algebraisation of the construction problem for classical superstring field theories in terms of homotopy algebras. Next, we solve the construction problem for open superstrings based on Witten's star product. The construction is recursive and involves a choice of homotopy operator for the zero mode of the η-ghost. It turns out that the solution can be extended to the Neveu-Schwarz subsectors of all superstring field theories. The recursive construction involves a hierarchy of string products at various picture deficits. The construction is not entirely natural, but it is argued that different choices give rise to solutions related by a field redefinition. Due to the presence of odd gluing parameters for Ramond states the extension to full superstring field theory is non-trivial. Instead, we construct gauge-invariant equations of motion for all superstring field theories. The realisation of spacetime supersymmetry in the open string sector is highly non-trivial and is described explicitly for the solution based on Witten's star product. After a field redefinition the non-polynomial equations of motion and the small Hilbert space constraint become polynomial. This polynomial system is shown to be supersymmetric. Quite interestingly, the supersymmetry algebra closes only up to gauge transformations. This indicates that only the physical phase space realizes N=1 supersymmetry. Apart from the algebraic constraints dictated by the geometry of supermoduli space the equations of motion or action should reproduce the traditional string S-matrix. The S-matrix of a field

  1. Geometric continuum regularization of quantum field theory

    International Nuclear Information System (INIS)

    Halpern, M.B.

    1989-01-01

    An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

  2. Statistical mechanics of lattice Boson field theory

    International Nuclear Information System (INIS)

    1976-01-01

    A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3 and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region

  3. Statistical mechanics of lattice boson field theory

    International Nuclear Information System (INIS)

    Baker, G.A. Jr.

    1977-01-01

    A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3, and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region. 24 references

  4. Cosmological viability of theories with massive spin-2 fields

    Energy Technology Data Exchange (ETDEWEB)

    Koennig, Frank

    2017-03-30

    Theories of spin-2 fields take on a particular role in modern physics. They do not only describe the mediation of gravity, the only theory of fundamental interactions of which no quantum field theoretical description exists, it furthermore was thought that they necessarily predict massless gauge bosons. Just recently, a consistent theory of a massive graviton was constructed and, subsequently, generalized to a bimetric theory of two interacting spin-2 fields. This thesis studies both the viability and consequences at cosmological scales in massive gravity as well as bimetric theories. We show that all consistent models that are free of gradient and ghost instabilities behave like the cosmological standard model, LCDM. In addition, we construct a new theory of massive gravity which is stable at both classical background and quantum level, even though it suffers from the Boulware-Deser ghost.

  5. Notes on the Verlinde formula in nonrational conformal field theories

    International Nuclear Information System (INIS)

    Jego, Charles; Troost, Jan

    2006-01-01

    We review and extend evidence for the validity of a generalized Verlinde formula, in particular, nonrational conformal field theories. We identify a subset of representations of the chiral algebra in nonrational conformal field theories that give rise to an analogue of the relation between modular S-matrices and fusion coefficients in rational conformal field theories. To that end we review and extend the Cardy-type brane calculations in bosonic and supersymmetric Liouville theory (and its duals) as well as in H 3 + . We analyze the three-point functions of Liouville theory and of H 3 + in detail to directly identify the fusion coefficients from the operator product expansion. Moreover, we check the validity of a proposed generic formula for localized brane one-point functions in nonrational conformal field theories

  6. A Unified Field Theory of Gravity, Electromagnetism, and theA Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field

    Directory of Open Access Journals (Sweden)

    Suhendro I.

    2008-01-01

    Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold $S_4$ via the connection, with the generalized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.

  7. Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

    Science.gov (United States)

    Tweney, Ryan D.

    2011-01-01

    James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other…

  8. Spontaneous symmetry breaking of (1+1)-dimensional φ4 theory in light-front field theory. II

    International Nuclear Information System (INIS)

    Pinsky, S.S.; van de Sande, B.

    1994-01-01

    We discuss spontaneous symmetry breaking of (1+1)-dimensional φ 4 theory in light-front field theory using a Tamm-Dancoff truncation. We show that, even though light-front field theory has a simple vacuum state which is an eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum expectation value. This occurs because the zero mode of the field must satisfy an operator-valued constraint equation. In the context of (1+1)-dimensional φ 4 theory we present solutions to the constraint equation using a Tamm-Dancoff truncation to a finite number of particles and modes. We study the behavior of the zero mode as a function of coupling and Fock space truncation. The zero mode introduces new interactions into the Hamiltonian which breaks the Z 2 symmetry of the theory when the coupling is stronger than the critical coupling. We investigate the energy spectrum in the symmetric and broken phases, show that the theory does not break down in the vicinity of the critical coupling, and discuss the connection to perturbation theory. Finally, we study the spectrum of the field φ and show that, in the broken phase, the field is localized away from φ=0 as one would expect from equal-time calculations. We explicitly show that tunneling occurs

  9. Unified field theory with Einsteinian photons and heavy bosons as field quants

    Energy Technology Data Exchange (ETDEWEB)

    Treder, H J

    1975-08-01

    After discussing previously the classical electrodynamics which corresponds to the quantum electrodynamics with two sorts of photons (photons with zero rest mass and nonvanishing rest mass), the general field theory of a vector field A/sup v/ with two sorts if field quanta is given. It is shown that the postulate for the ''unity of the four-current'' determining the physical contents of this theory makes it possible to regard it as a classical ansatz of a unified theory of the electromagnetic and the weak interactions. From the ''unity of the currents'' results that the electrons are delta-like point-particles with a finite self-potential and finite field masses M = epsilon/sup 2//2 kc/sup -2/. The Compton wave-length of the heavy photons k/sup -1/ = h/mc has the meaning of an ''elementary length'' of the electromagnetic interactions and the rest mass m = khc/sup -1/ of these bosons is of the order of a baryon mass. (auth)

  10. Conformal field theory and 2D critical phenomena. Part 1

    International Nuclear Information System (INIS)

    Zamolodchikov, A.B.; Zamolodchikov, Al.B.

    1989-01-01

    Review of the recent developments in the two-dimensional conformal field theory and especially its applications to the physics of 2D critical phenomena is given. It includes the Ising model, the Potts model. Minimal models, corresponding to theories invariant under higher symmetries, such as superconformal theories, parafermionic theories and theories with current and W-algebras are also discussed. Non-hamiltonian approach to two-dimensional field theory is formulated. 126 refs

  11. Conformal quantum field theory: From Haag-Kastler nets to Wightman fields

    International Nuclear Information System (INIS)

    Joerss, M.

    1996-07-01

    Starting from a chiral conformal Haag-Kastler net of local observables on two-dimensional Minkowski space-time, we construct associated pointlike localizable charged fields which intertwine between the superselection sectors with finite statistics of the theory. This amounts to a proof of the spin-statistics theorem, the PCT theorem, the Bisognano-Wichmann identification of modular operators, Haag duality in the vacuum sector, and the existence of operator product expansions. Our method consists of the explicit use of the representation theory of the universal covering group of SL(2,R). A central role is played by a ''conformal cluster theorem'' for conformal two-point functions in algebraic quantum field theory. Generalizing this ''conformal cluster theorem'' to the n-point functions of Haag-Kastler theories, we can finally construct from a chiral conformal net of algebras a compelte set of conformal n-point functions fulfilling the Wightman axioms. (orig.)

  12. Topics in quantum field theory; Topicos em teoria quantica dos campos

    Energy Technology Data Exchange (ETDEWEB)

    Svaiter, N.F

    2006-11-15

    This paper presents some important aspects on quantum field theory, covering the following aspects: the triumph and limitations of the quantum field theory; the field theory in curved spaces - Hawking and Unruh-Davies effects; the problem of divergent theory of the zero-point; the problem of the spinning detector and the Trocheries-Takeno vacuum; the field theory at finite temperature - symmetry breaking and phase transition; the problem of the summability of the perturbative series and the perturbative expansion for the strong coupling; quantized fields in presence of classical macroscopic structures; the Parisi-Wu stochastic quantization method.

  13. Topological field theories and duality

    International Nuclear Information System (INIS)

    Stephany, J.; Universidad Simon Bolivar, Caracas

    1996-05-01

    Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifold are discussed in a simple example, and their relation with the properties of Topological Field Theories is established. (author). 16 refs

  14. Quantum field theory and link invariants

    International Nuclear Information System (INIS)

    Cotta-Ramusino, P.; Guadagnini, E.; Mintchev, M.; Martellini, M.

    1990-01-01

    A skein relation for the expectation values of Wilson line operators in three-dimensional SU(N) Chern-Simons gauge theory is derived at first order in the coupling constant. We use a variational method based on the properties of the three-dimensional field theory. The relationship between the above expectation values and the known link invariants is established. (orig.)

  15. Towards chaos criterion in quantum field theory

    OpenAIRE

    Kuvshinov, V. I.; Kuzmin, A. V.

    2002-01-01

    Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.

  16. Warped conformal field theory as lower spin gravity

    Science.gov (United States)

    Hofman, Diego M.; Rollier, Blaise

    2015-08-01

    Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL (2, R) × U (1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.

  17. Warped conformal field theory as lower spin gravity

    Directory of Open Access Journals (Sweden)

    Diego M. Hofman

    2015-08-01

    Full Text Available Two dimensional Warped Conformal Field Theories (WCFTs may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space–times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton–Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL(2,R×U(1 Chern–Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.

  18. On the derivation of effective field theories

    International Nuclear Information System (INIS)

    Uzunov, Dimo I.

    2004-12-01

    A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of cumulant expansion leads to a new point of view on the effective field theories. The proposed approach can be used for a systematic treatment of fluctuation effects of various length scales and, perhaps, for the development of a new coarse graining procedure. We outline and justify our method by some preliminary calculations. Concrete results are given for the critical temperature and the Landau parameters of the φ 4 -theory - the field counterpart of the Ising model. An important unresolved problem of the modern theory of phase transitions - the problem for the calculation of the true critical temperature, is considered within the framework of the present approach. A comprehensive description of the ground state properties of many-body systems is also demonstrated. (author)

  19. Boundary conformal field theory and the worldsheet approach to D-branes

    CERN Document Server

    Recknagel, Andreas

    2013-01-01

    Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the framework allows discussion of strings and branes directly at the quantum level. Written by internationally renowned experts, this comprehensive introduction to boundary conformal field theory reaches from theoretical foundations to recent developments, with an emphasis on the algebraic treatment of string backgrounds. Topics covered include basic concepts in conformal field theory with and without boundaries, the mathematical description of strings and D-branes, and the geometry of strongly curved spacetime. The book offers insights into string geometry that go beyond classical notions. Describing the theory from basic concepts, and providing numerous worked examples from conformal field theory and string theory, this reference is of interest to graduate students and...

  20. Renormalization and Interaction in Quantum Field Theory

    International Nuclear Information System (INIS)

    RATSIMBARISON, H.M.

    2008-01-01

    This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory. [fr

  1. Algebraic construction of interacting higher spin field theories

    International Nuclear Information System (INIS)

    Fougere, F.

    1991-10-01

    We develop a general framework which we believe may provide some insights into the structure of interacting 'high spin' field theories. A finite or infinite set of classical spin fields is described by means of a field defined on an enlarged spacetime manifold. The free action and its gauge symmetries are gathered into a nilpotent differential operator on this manifold. In particular, the choice of Grassmann-valued extra coordinates leads to theories involving only a finite set of fields, the possible contents (spin multiplicities, degree of reducibility, etc.) of which are classified according to the representations of a unitary algebra. The interacting theory is characterized by a functional of the field on the enlarged manifold. We show that there is among these functionals a natural graded Lie algebra structure allowing one to rewrite the gauge invariance condition of the action in a concise form which is a nonlinear generalization of the nilpotency condition of the free theory. We obtain the general solution of this 'classical master equation' , which can be built recurrently starting form the cubic vertex, and we study its symmetries. Our formalism lends itself to a systematic introduction of additional conditions, such as locality, polynomiality, etc. We write down the general form of the solutions exhibiting a scale invariance. The case of a spin 1 field yields, as a unique solution, Yang-Mills theory. In view of quantization, we show that the solution of the classical master equation straightforwardly provides a solution of the (quantum) Batalin-Vilkoviski master equation. One may then obtain a gauge fixed action in the usual way

  2. Introductory lectures on conformal field theory and strings

    International Nuclear Information System (INIS)

    Randjbar-Daemi, S.; Strathdee, J.

    1990-01-01

    The aim of these lectures is to provide an introduction to a first quantized formulation of string theory. This amounts to developing a consistent set of prescriptions for the perturbative computation of on-shell string amplitudes. The principal tool in this development is 2-dimensional conformal field theory on oriented manifolds of finite genus without boundaries (we treat only closed strings). This class of theory is much simpler than 4-dimensional quantum gravity with which it has many similarities. The geometry is not dynamical in this case, and the matter fields are not sensitive to local features of the geometry but only to global properties which can be characterized by a finite set of parameters (moduli). This can be formulated as field theory on a Riemann surface. We specialize mainly to free field theories for which the quantization problem can be completely solved by elementary means. An introduction to the general case will be given in Lectures II and III where the algebraic approach is discussed. The mathematics of Riemann surfaces is a well developed subject whose formalism is reviewed along with some of the principal theorems in Lecture IV. Physical string states are realized in the Hilbert space of a conformal field theory by the action of so-called ''vertex operators'' on the field theory vacuum state. Correlation functions of these vertex operators serve as ingredients for the computation of string amplitudes. They are to be integrated so as to include the contributions of all conformally inequivalent geometries, and a further manipulation (the GSO projection) is to be performed. These steps are to be regarded as part of the string prescription. The are introduced ad hoc to meet invariance and unitarity requirements. However, in these introductory lectures we give a description only of the integration over geometries (Lecture VII). The GSO projection, and related questions of modular invariance and unitarity are beyond the scope of these lectures

  3. Introductory lectures on Conformal Field Theory and Strings

    International Nuclear Information System (INIS)

    Randjbar-Daemi, S.; Strathdee, J.

    1990-01-01

    The aim of these lectures is to provide an introduction to a first quantized formulation of string theory. This amounts to developing a consistent set of prescriptions for the perturbative computation of on-shell string amplitudes. The principal tool in this development is 2-dimensional conformal field theory on oriented manifolds of finite genus without boundaries (we treat only closed strings). This class of theory is much simpler than 4-dimensional quantum gravity with which it has many similarities. The geometry is not dynamical in this case, and the matter fields are not sensitive to local features of the geometry but only to global properties which can be characterized by a finite set of parameters (moduli). This can be formulated as field theory on a Riemann surface. We specialize mainly to free field theories for which the quantization problem can be completely solved by elementary means. An introduction to the general case will be given in Lectures II and III where the algebraic approach is discussed. The mathematics of Riemann surfaces is a well developed subject whose formalism is reviewed along with some of the principal theorems in Lecture IV. Physical string states are realized in the Hilbert space of a conformal field theory by the action of so-called ''vertex operators'' on the field theory vacuum state. Correlation functions of these vertex operators serve as ingredients for the computation of string amplitudes. They are to be integrated so as to include the contributions of all conformally inequivalent geometries, and a further manipulation (the GSO projection) is to be performed. These steps are to be regarded as part of the string prescription. They are introduced ad hoc to meet invariance and unitarity requirements. However, in these introductory lectures we give a description only of the integration over geometries (Lecture VII). The GSO projection, and related questions of modular invariance and unitarity are beyond the scope of these

  4. Supersymmetric rings in field theory

    International Nuclear Information System (INIS)

    Blanco-Pillado, Jose J.; Redi, Michele

    2006-01-01

    We study the dynamics of BPS string-like objects obtained by lifting monopole and dyon solutions of N = 2 Super-Yang-Mills theory to five dimensions. We present exact traveling wave solutions which preserve half of the supersymmetries. Upon compactification this leads to macroscopic BPS rings in four dimensions in field theory. Due to the fact that the strings effectively move in six dimensions the same procedure can also be used to obtain rings in five dimensions by using the hidden dimension

  5. Numerical analysis of electromagnetic fields

    CERN Document Server

    Zhou Pei Bai

    1993-01-01

    Numerical methods for solving boundary value problems have developed rapidly. Knowledge of these methods is important both for engineers and scientists. There are many books published that deal with various approximate methods such as the finite element method, the boundary element method and so on. However, there is no textbook that includes all of these methods. This book is intended to fill this gap. The book is designed to be suitable for graduate students in engineering science, for senior undergraduate students as well as for scientists and engineers who are interested in electromagnetic fields. Objective Numerical calculation is the combination of mathematical methods and field theory. A great number of mathematical concepts, principles and techniques are discussed and many computational techniques are considered in dealing with practical problems. The purpose of this book is to provide students with a solid background in numerical analysis of the field problems. The book emphasizes the basic theories ...

  6. Irreversibility and higher-spin conformal field theory

    Science.gov (United States)

    Anselmi, Damiano

    2000-08-01

    I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.

  7. Superconvergent perturbation theory for euclidean scalar field theories

    International Nuclear Information System (INIS)

    Ushveridze, A.G.

    1984-01-01

    It is shown that the bare (unrenormalized) correlation functions in the euclidean scalar field theories can be expanded in a series whose terms, being computable in a relatively simple way, are free from ultraviolet and infrared divergencies. This series is convergent (divergent) for finite (infinite) values of the correlation functions. (orig.)

  8. Microcanonical formulation of quantum field theories

    International Nuclear Information System (INIS)

    Iwazaki, A.

    1984-03-01

    A microcanonical formulation of Euclidean quantum field theories is presented. In the formulation, correlation functions are given by a microcanonical ensemble average of fields. Furthermore, the perturbative equivalence of the formulation and the standard functional formulation is proved and the equipartition low is derived in our formulation. (author)

  9. Effective field theory of interactions on the lattice

    DEFF Research Database (Denmark)

    Valiente, Manuel; Zinner, Nikolaj T.

    2015-01-01

    We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare lattice coupling constants to the continuum coupling consta...... constants. Our method constitutes a very simple avenue for the systematic renormalization in effective field theory, and is especially useful as the number of interaction parameters increases.......We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare lattice coupling constants to the continuum coupling...

  10. Logarithmic conformal field theory: beyond an introduction

    International Nuclear Information System (INIS)

    Creutzig, Thomas; Ridout, David

    2013-01-01

    This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with the remarkable observation of Cardy that the horizontal crossing probability of critical percolation may be computed analytically within the formalism of boundary conformal field theory. Cardy’s derivation relies on certain implicit assumptions which are shown to lead inexorably to indecomposable modules and logarithmic singularities in correlators. For this, a short introduction to the fusion algorithm of Nahm, Gaberdiel and Kausch is provided. While the percolation logarithmic conformal field theory is still not completely understood, there are several examples for which the formalism familiar from rational conformal field theory, including bulk partition functions, correlation functions, modular transformations, fusion rules and the Verlinde formula, has been successfully generalized. This is illustrated for three examples: the singlet model M(1,2), related to the triplet model W(1,2), symplectic fermions and the fermionic bc ghost system; the fractional level Wess–Zumino–Witten model based on sl-hat (2) at k=−(1/2), related to the bosonic βγ ghost system; and the Wess–Zumino–Witten model for the Lie supergroup GL(1∣1), related to SL(2∣1) at k=−(1/2) and 1, the Bershadsky–Polyakov algebra W 3 (2) and the Feigin–Semikhatov algebras W n (2) . These examples have been chosen because they represent the most accessible, and most useful, members of the three best-understood families of logarithmic conformal field theories. The logarithmic minimal models W(q,p), the fractional level Wess–Zumino–Witten models, and the Wess–Zumino–Witten models on Lie supergroups (excluding OSP(1∣2n)). In this review, the emphasis lies on the representation theory of the underlying chiral algebra and the modular data pertaining to the characters of the representations. Each of the archetypal logarithmic conformal field theories is

  11. Supersymmetric gauge theories, quantization of Mflat, and conformal field theory

    International Nuclear Information System (INIS)

    Teschner, J.; Vartanov, G.S.

    2013-02-01

    We propose a derivation of the correspondence between certain gauge theories with N=2 supersymmetry and conformal field theory discovered by Alday, Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain results from the literature we argue that the quantum theory of the moduli spaces of flat SL(2,R)-connections represents a nonperturbative ''skeleton'' of the gauge theory, protected by supersymmetry. It follows that instanton partition functions can be characterized as solutions to a Riemann-Hilbert type problem. In order to solve it, we describe the quantization of the moduli spaces of flat connections explicitly in terms of two natural sets of Darboux coordinates. The kernel describing the relation between the two pictures represents the solution to the Riemann Hilbert problem, and is naturally identified with the Liouville conformal blocks.

  12. Non-Abelian gauge theory of fields associated with dyons

    International Nuclear Information System (INIS)

    Rajput, B.S.; Kumar, S.R.

    1983-01-01

    A suitable Lorentz invariant non-Abelian gauge theory of the fields associated with dyons has been constructed to describe the dual dynamics between colour isocharges and topological charges. It has been shown that the generalized particle current is gauge covariant and not conserved in non-Abelian theory. It has also been shown that in this theory the unphysical string variables and unphysical charged fields are not needed and that any extra constraint to maintain the dual symmetry of field equation and Lagrangian is also not needed. (author)

  13. Polyacetylene and relativistic field-theory models

    International Nuclear Information System (INIS)

    Bishop, A.R.; Campbell, D.K.; Fesser, K.

    1981-01-01

    Connections between continuum, mean-field, adiabatic Peierls-Froehlich theory in the half-filled band limit and known field theory results are discussed. Particular attention is given to the phi 4 model and to the solvable N = 2 Gross-Neveu model. The latter is equivalent to the Peierls system at a static, semi-classical level. Based on this equivalence we note the prediction of both kink and polaron solitons in models of trans-(CH)/sub x/. Polarons in cis-(CH)/sub x/ are compared with those in the trans isomer. Optical absorption from polarons is described, and general experimental consequences of polarons in (CH)/sub x/ and other conjugated polymers is discussed

  14. Schroedinger representation in quantum field theory

    International Nuclear Information System (INIS)

    Luescher, M.

    1985-01-01

    Until recently, the Schroedinger representation in quantum field theory had not received much attention, even more so because there were reasons to believe that in the presence of interactions it did not exist in a mathematically well-defined sense. When Symanzik set out to solve this problem, he was motivated by a special 2-dimensional case, the relativistic string model, in which the Schroedinger wave functionals are the primary objects of physical interest. Also, he knew that if it were possible to demonstrate the existence of the Schroedinger representation, the (then unproven) ultraviolet finiteness of the Casimir force in renormalizable quantum field theories would probably follow. (orig./HSI)

  15. The topology of Double Field Theory

    Science.gov (United States)

    Hassler, Falk

    2018-04-01

    We describe the doubled space of Double Field Theory as a group manifold G with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so G only captures the topology of the doubled space. Strong Constraint solutions are maximal isotropic submanifold M in G. We construct them and their Generalized Geometry in Double Field Theory on Group Manifolds. In general, G admits different physical subspace M which are Poisson-Lie T-dual to each other. By studying two examples, we reproduce the topology changes induced by T-duality with non-trivial H-flux which were discussed by Bouwknegt, Evslin and Mathai [1].

  16. Unified theory of gravitation, electromagnetism, and the Yang-Mills field

    International Nuclear Information System (INIS)

    Borchsenius, K.

    1976-01-01

    The recent modification and extension of Einstein's nonsymmetric unified field theory for gravitation and electromagnetism is generalized to include the Yang-Mills field theory. The generalization consists in assuming that the components of the linear connection and of the fundamental tensor are not ordinary c numbers but are matrices related to some unitary symmetry. As an example we consider the SU(2) case. The theory is applied to the gauge-covariant formulation of electrically and isotopically charged spin-1/2 field theories

  17. The topology of moduli space and quantum field theory

    International Nuclear Information System (INIS)

    Montano, D.; Sonnenschein, J.

    1989-01-01

    We show how an SO(2,1) gauge theory with a fermionic symmetry may be used to describe the topology of the moduli space of curves. The observables of the theory correspond to the generators of the cohomology of moduli space. This is an extension of the topological quantum field theory introduced by Witten to investigate the cohomology of Yang-Mills instanton moduli space. We explore the basic structure of topological quantum field theories, examine a toy U(1) model, and then realize a full theory of moduli space topology. We also discuss why a pure gravity theory, as attempted in previous work, could not succeed. (orig.)

  18. Supersymmetry for gauged double field theory and generalised Scherk–Schwarz reductions

    International Nuclear Information System (INIS)

    Berman, David S.; Lee, Kanghoon

    2014-01-01

    Previous constructions of supersymmetry for double field theory have relied on the so-called strong constraint. In this paper, the strong constraint is relaxed and the theory is shown to possess supersymmetry once the generalised Scherk–Schwarz reduction is imposed. The equivalence between the generalised Scherk–Schwarz reduced theory and the gauged double field theory is then examined in detail for the supersymmetric theory. As a biproduct we write the generalised Killing spinor equations for the supersymmetric double field theory

  19. Finiteness of quantum field theories and supersymmetry

    International Nuclear Information System (INIS)

    Lucha, W.; Neufeld, H.

    1986-01-01

    We study the consequences of finiteness for a general renormalizable quantum field theory by analysing the finiteness conditions resulting from the requirement of absence of divergent contributions to the renormalizations of the parameters of an arbitrary gauge theory. In all cases considered, the well-known two-loop finite supersymmetric theories prove to be the unique solution of the finiteness criterion. (Author)

  20. Associative-algebraic approach to logarithmic conformal field theories

    International Nuclear Information System (INIS)

    Read, N.; Saleur, Hubert

    2007-01-01

    We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non-semisimple associative algebras appearing in their lattice regularizations (as discussed in a companion paper [N. Read, H. Saleur, Enlarged symmetry algebras of spin chains, loop models, and S-matrices, cond-mat/0701259]). Here we work out in detail two examples of theories derived as the continuum limit of XXZ spin-1/2 chains, which are related to spin chains with supersymmetry algebras gl(n|n) and gl(n+1 vertical bar n), respectively, with open (or free) boundary conditions in all cases. These theories can also be viewed as vertex models, or as loop models. Their continuum limits are boundary conformal field theories (CFTs) with central charge c=-2 and c=0 respectively, and in the loop interpretation they describe dense polymers and the boundaries of critical percolation clusters, respectively. We also discuss the case of dilute (critical) polymers as another boundary CFT with c=0. Within the supersymmetric formulations, these boundary CFTs describe the fixed points of certain nonlinear sigma models that have a supercoset space as the target manifold, and of Landau-Ginzburg field theories. The submodule structures of indecomposable representations of the Virasoro algebra appearing in the boundary CFT, representing local fields, are derived from the lattice. A central result is the derivation of the fusion rules for these fields

  1. Physical states at the tachyonic vacuum of open string field theory

    International Nuclear Information System (INIS)

    Giusto, S.; Imbimbo, C.

    2004-01-01

    We illustrate a method for computing the number of physical states of open string theory at the stable tachyonic vacuum in level truncation approximation. The method is based on the analysis of the gauge-fixed open string field theory quadratic action that includes Fadeev-Popov ghost string fields. Computations up to level 9 in the scalar sector are consistent with Sen's conjecture about the absence of physical open string states at the tachyonic vacuum. We also derive a long exact cohomology sequence that relates relative and absolute cohomologies of the BRS operator at the non-perturbative vacuum. We use this exact result in conjunction with our numerical findings to conclude that the higher ghost number non-perturbative BRS cohomologies are non-empty

  2. Renormalization group study of scalar field theories

    International Nuclear Information System (INIS)

    Hasenfratz, A.; Hasenfratz, P.

    1986-01-01

    An approximate RG equation is derived and studied in scalar quantum field theories in d dimensions. The approximation allows for an infinite number of different couplings in the potential, but excludes interactions containing derivatives. The resulting non-linear partial differential equation can be studied by simple means. Both the gaussian and the non-gaussian fixed points are described qualitatively correctly by the equation. The RG flows in d=4 and the problem of defining an ''effective'' field theory are discussed in detail. (orig.)

  3. Classical theory of electric and magnetic fields

    CERN Document Server

    Good, Roland H

    1971-01-01

    Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma

  4. High-electric-field quantum transport theory for semiconductor superlattices

    International Nuclear Information System (INIS)

    Nguyen Hong Shon; Nazareno, H.N.

    1995-12-01

    Based on the Baym-Kadanoff-Keldysh nonequilibrium Green's functions technique, a quantum transport theory for semiconductor superlattices under high-electric field is developed. This theory is capable of considering collisional broadening, intra-collisional field effects and band transport and hopping regimes simultaneously. Numerical calculations for narrow-miniband superlattices in high electric field, when the hopping regime dominates are in reasonable agreement with experimental results and show a significant deviation from the Boltzmann theory. A semiphenomenological formula for current density in hopping regime is proposed. (author). 60 refs, 4 figs

  5. Field theory of the spinning electron: Internal motions

    OpenAIRE

    Salesi, Giovanni; Recami, Erasmo

    1996-01-01

    We present here a field theory of the spinning electron, by writing down a new equation for the 4-velocity field v^mu (different from that of Dirac theory), which allows a classically intelligible description of the electron. Moreover, we make explicit the noticeable kinematical properties of such velocity field (which also result different from the ordinary ones). At last, we analyze the internal zitterbewegung (zbw) motions, for both time-like and light-like speeds. We adopt in this paper t...

  6. Nonlocal quantum field theory and stochastic quantum mechanics

    International Nuclear Information System (INIS)

    Namsrai, K.

    1986-01-01

    This volume presents a systematic development of the implications to both quantum mechanics and quantum field theory of the hypothesis of a stochastic structure of space-time. Some applications to elementary particle physics are also considered. Part 1 is concerned with nonlocal quantum field theory and, among other topics, deals with quantized fields, electromagnetic and weak processes, the Schroedinger equation, and functional methods and their applications. Part 2 presents an introduction to stochastic mechanics and many specific problems of interest are discussed. (Auth.)

  7. An introduction to nonlinear analysis and fixed point theory

    CERN Document Server

    Pathak, Hemant Kumar

    2018-01-01

    This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for ...

  8. Meta-orbital transition in heavy-fermion systems. Analysis by dynamical mean field theory and self-consistent renormalization theory of orbital fluctuations

    International Nuclear Information System (INIS)

    Hattori, Kazumasa

    2010-01-01

    We investigate a two-orbital Anderson lattice model with Ising orbital intersite exchange interactions on the basis of a dynamical mean field theory combined with the static mean field approximation of intersite orbital interactions. Focusing on Ce-based heavy-fermion compounds, we examine the orbital crossover between two orbital states, when the total f-electron number per site n f is ∼1. We show that a 'meta-orbital' transition, at which the occupancy of two orbitals changes steeply, occurs when the hybridization between the ground-state f-electron orbital and conduction electrons is smaller than that between the excited f-electron orbital and conduction electrons at low pressures. Near the meta-orbital critical end point, orbital fluctuations are enhanced and couple with charge fluctuations. A critical theory of meta-orbital fluctuations is also developed by applying the self-consistent renormalization theory of itinerant electron magnetism to orbital fluctuations. The critical end point, first-order transition, and crossover are described within Gaussian approximations of orbital fluctuations. We discuss the relevance of our results to CeAl 2 , CeCu 2 Si 2 , CeCu 2 Ge 2 , and related compounds, which all have low-lying crystalline-electric-field excited states. (author)

  9. Lattice formulations of supersymmetric gauge theories with matter fields

    International Nuclear Information System (INIS)

    Joseph, Anosh

    2014-12-01

    Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact supersymmetric. We discuss the recent lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields in various representations of the color group.

  10. Globally and locally supersymmetric effective theories for light fields

    CERN Document Server

    Brizi, Leonardo; Scrucca, Claudio A

    2009-01-01

    We reconsider the general question of how to characterize most efficiently the low-energy effective theory obtained by integrating out heavy modes in globally and locally supersymmetric theories. We consider theories with chiral and vector multiplets and identify the conditions under which an approximately supersymmetric low-energy effective theory can exist. These conditions translate into the requirements that all the derivatives, fermions and auxiliary fields should be small in units of the heavy mass scale. They apply not only to the matter sector, but also to the gravitational one if present, and imply in that case that the gravitino mass should be small. We then show how to determine the unique exactly supersymmetric theory that approximates this effective theory at the lowest order in the counting of derivatives, fermions and auxiliary fields, by working both at the superfield level and with component fields. As a result we give a simple prescription for integrating out heavy superfields in an algebrai...

  11. Infinite additional symmetries in two-dimensional conformal quantum field theory

    International Nuclear Information System (INIS)

    Zamolodchikov, A.B.

    1986-01-01

    This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form associative algebras with quadratic determining relations. ''Minimal models'' of conforma field theory with such additional symmetries are considered. The space of local fields occurring in a conformal field theory with additional symmetry corresponds to a certain (in general, reducible) representation of the corresponding algebra of the symmetry

  12. Supergravity, Non-Conformal Field Theories and Brane-Worlds

    CERN Document Server

    Gherghetta, Tony; Gherghetta, Tony; Oz, Yaron

    2002-01-01

    We consider the supergravity dual descriptions of non-conformal super Yang-Mills theories realized on the world-volume of Dp-branes. We use the dual description to compute stress-energy tensor and current correlators. We apply the results to the study of dilatonic brane-worlds described by non-conformal field theories coupled to gravity. We find that brane-worlds based on D4 and D5 branes exhibit a localization of gauge and gravitational fields. We calculate the corrections to the Newton and Coulomb laws in these theories.

  13. Exact results for integrable asymptotically-free field theories

    CERN Document Server

    Evans, J M; Evans, Jonathan M; Hollowood, Timothy J

    1995-01-01

    An account is given of a technique for testing the equivalence between an exact factorizable S-matrix and an asymptotically-free Lagrangian field theory in two space-time dimensions. The method provides a way of resolving CDD ambiguities in the S-matrix and it also allows for an exact determination of the physical mass in terms of the Lambda parameter of perturbation theory. The results for various specific examples are summarized. (To appear in the Proceedings of the Conference on Recent Developments in Quantum Field Theory and Statistical Mechanics, ICTP, Trieste, Easter 1995).

  14. Exact marginality in open string field theory. A general framework

    International Nuclear Information System (INIS)

    Kiermaier, M.

    2007-07-01

    We construct analytic solutions of open bosonic string field theory for any exactly marginal deformation in any boundary conformal field theory when properly renormalized operator products of the marginal operator are given. We explicitly provide such renormalized operator products for a class of marginal deformations which include the deformations of flat D-branes in flat backgrounds by constant massless modes of the gauge field and of the scalar fields on the D-branes, the cosine potential for a space-like coordinate, and the hyperbolic cosine potential for the time-like coordinate. In our construction we use integrated vertex operators, which are closely related to finite deformations in boundary conformal field theory, while previous analytic solutions were based on unintegrated vertex operators. We also introduce a modified star product to formulate string field theory around the deformed background. (orig.)

  15. The foliation operator in history quantum field theory

    International Nuclear Information System (INIS)

    Isham, C.J.; Savvidou, K.

    2002-01-01

    As a preliminary to discussing the quantization of the foliation in a history form of general relativity, we show how the discussion in an earlier work [J. Math. Phys. 43, 3053 (2002)] of a history version of free, scalar quantum field theory can be augmented in such a way as to include the quantization of the unit-length, timelike vector that determines a Lorentzian foliation of Minkowski space-time. We employ a Hilbert bundle construction that is motivated by (i) discussing the role of the external Lorentz group in the existing history quantum field theory [J. Math. Phys. 43, 3053 (2002)] and (ii) considering a specific representation of the extended history algebra obtained from the multi-symplectic representation of scalar field theory

  16. Ultraviolet stability of three-dimensional lattice pure gauge field theories

    International Nuclear Information System (INIS)

    Balaban, T.

    1985-01-01

    We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories. (orig.)

  17. Quantum field theory III. Gauge theory. A bridge between mathematicians and physicists

    International Nuclear Information System (INIS)

    Zeidler, Eberhard

    2011-01-01

    In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). (orig.)

  18. Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

    Science.gov (United States)

    Antonowicz, Marek; Szczyrba, Wiktor

    1985-06-01

    We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

  19. Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

    International Nuclear Information System (INIS)

    Antonowicz, M.; Szczyrba, W.

    1985-01-01

    We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8 = 12 independent degrees of freedom in the phase space

  20. Unitarity Bounds and RG Flows in Time Dependent Quantum Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC

    2012-04-05

    We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-N double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.