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

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)

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

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.)

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.

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)

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.)

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.

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.)

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.

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

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

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

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

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

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)

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

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.)

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

Hamiltonian lattice studies of chiral meson field theories

International Nuclear Information System (INIS)

Chin, S.A.

1998-01-01

The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin lattice system with quantum fluctuations. The result is an interesting marriage between quantum many-body theory and classical spin systems. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In a variational 16 3 lattice study, the ground state chiral phase transition is shown to be first order. Moreover, as the chiral phase transition is approached, the mass gap of pionic collective modes with quantum number of the ω vector meson drops toward zero. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)

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.)

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

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 ...

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.

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...

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.)

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.)

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.

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

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.

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.)

Progress on study of nuclear data theory and related fields at the Theory Group of CNDC

Energy Technology Data Exchange (ETDEWEB)

Zhigang, Ge [China Nuclear Data Center, CIAE (China)

1996-06-01

The Theory Group of CNDC (China Nuclear Data Center) has made a lot of progress in nuclear reaction theory and its application as well as many other related fields in 1995. The recent progress in nuclear reaction theory study and its applications, the recent progress in the nuclear data calculation and related code development are introduced. The production rate of radioactive nuclear beam induced by 70 MeV protons on {sup 72}Ge target were calculated. The calculated results are presented.

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)

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

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

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.

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

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)

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.

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.)

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.)

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)

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.)

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.

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...

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.)

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

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)

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.)

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

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)

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

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

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

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)

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.

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.

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

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

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

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.

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.

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.)

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'.

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

Analytic study of nonperturbative solutions in open string field theory

International Nuclear Information System (INIS)

Bars, I.; Kishimoto, I.; Matsuo, Y.

2003-01-01

We propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution

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)

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.)

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

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.

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...

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

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

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

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

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.)

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

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.

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

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.)

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.)

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

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

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.)

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)

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.

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.)

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.

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

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)

Bjorken-Johnson-Low technique and perturbation study on chiral anomaly in abelian coset pure gauge field theory

International Nuclear Information System (INIS)

Jing Sicong; Ruan Jie; AH. Dept. of Modern Physics)

1990-01-01

The perturbation theory in coset pure gauge field theory is studied for the first time. By using the Bjorken-johnson-Low technique and calculating the Schwinger term in related commutators, the anomalous Ward identity in Abelian coset pure gauge field theory is derived, which is consistent with the non-perutrbative calculation

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

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)

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

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

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

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.

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)

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.

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.

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.)

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

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.

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

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

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

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.)

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

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.

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.

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

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.

[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

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)

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.

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.)

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

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

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

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...

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...

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

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.

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

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...

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

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

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

Introduction to the renormalization group study in relativistic quantum field theory

International Nuclear Information System (INIS)

Mignaco, J.A.; Roditi, I.

1985-01-01

An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.) [pt

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)

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)

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...

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.)

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...

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...

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

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.)

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.

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)

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.

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)

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.

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.

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

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.)

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

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.

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.

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

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.

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.)

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.)

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

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

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

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

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.

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)

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

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.)

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.)

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.)

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.)

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

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)

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)

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)

Wilson lines in quantum field theory

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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.

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.

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

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

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.

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

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.)

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.

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

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.

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...

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

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

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

Topics in quantum field theory and cosmology

International Nuclear Information System (INIS)

Brandenberger, R.H.

1983-01-01

This thesis contains a study of topics in quantum field theory and cosmology in the context of the new inflationary universe scenario. It presents a review of the quantum field theory methods used in the new cosmological models. The following chapters are a detailed study of energy density fluctuations in the early universe. Hawking radiation is derived as the source of initial perturbations in two complementary ways. The following section presents a new gauge invariant framework to study the growth of fluctuations outside the horizon. This framework is applied to the new inflationary universe in the final chapter. The introduction gives a brief outline of the new cosmological models

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

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)

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.

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

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)

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…

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].

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.

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

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.

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

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

On the field/string theory approach to theta dependence in large N Yang-Mills theory

International Nuclear Information System (INIS)

Gabadadze, Gregory

1999-01-01

The theta dependence of the vacuum energy in large N Yang-Mills theory has been studied some time ago by Witten using a duality of large N gauge theories with the string theory compactified on a certain space-time. We show that within the field theory context vacuum fluctuations of the topological charge give rise to the vacuum energy consistent with the string theory computation. Furthermore, we calculate 1/N suppressed corrections to the string theory result. The reconciliation of the string and field theory approaches is based on the fact that the gauge theory instantons carry zerobrane charge in the corresponding D-brane construction of Yang-Mills theory. Given the formula for the vacuum energy we study certain aspects of stability of the false vacua of the model for different realizations of the initial conditions. The vacuum structure appears to be different depending on whether N is infinite or, alternatively, large but finite

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

Numerical calculations in quantum field theories

International Nuclear Information System (INIS)

Rebbi, C.

1984-01-01

Four lecture notes are included: (1) motivation for numerical calculations in Quantum Field Theory; (2) numerical simulation methods; (3) Monte Carlo studies of Quantum Chromo Dynamics; and (4) systems with fermions. 23 references

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.

Conformal field theory with two kinds of Bosonic fields and two linear dilatons

International Nuclear Information System (INIS)

Kamani, Davoud

2010-01-01

We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable to study a more general case. Various properties of the model such as OPEs, central charge, conformal properties of the fields and associated algebras will be studied. (author)

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

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

Anomaly cancelation in field theory and F-theory on a circle

International Nuclear Information System (INIS)

Grimm, Thomas W.; Kapfer, Andreas

2016-01-01

We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.

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

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.

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.

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)

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)

Representation theory of current algebra and conformal field theory on Riemann surfaces

International Nuclear Information System (INIS)

Yamada, Yasuhiko

1989-01-01

We study conformal field theories with current algebra (WZW-model) on general Riemann surfaces based on the integrable representation theory of current algebra. The space of chiral conformal blocks defined as solutions of current and conformal Ward identities is shown to be finite dimensional and satisfies the factorization properties. (author)

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.

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

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

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

Statistical field theory of futures commodity prices

Science.gov (United States)

Baaquie, Belal E.; Yu, Miao

2018-02-01

The statistical theory of commodity prices has been formulated by Baaquie (2013). Further empirical studies of single (Baaquie et al., 2015) and multiple commodity prices (Baaquie et al., 2016) have provided strong evidence in support the primary assumptions of the statistical formulation. In this paper, the model for spot prices (Baaquie, 2013) is extended to model futures commodity prices using a statistical field theory of futures commodity prices. The futures prices are modeled as a two dimensional statistical field and a nonlinear Lagrangian is postulated. Empirical studies provide clear evidence in support of the model, with many nontrivial features of the model finding unexpected support from market data.

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

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

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)

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

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

(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)

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)

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)

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

Vortex operators in gauge field theories

International Nuclear Information System (INIS)

Polchinski, J.

1980-07-01

Several related aspects of the 't Hooft vortex operator are studied. The current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator are reviewed first. The Abelian vortex operator written in terms of elementary fields and the calculation of its Green's functions are considered. A two-dimensional solvable model of a Dirac string is presented. The expression of the Green's functions more neatly in terms of Wu and Yang's geometrical idea of sections is addressed. The renormalization of the Green's functions of two kinds of Abelian looplike operators, the Wilson loop and the vortex operator, is studied; for both operators only an overall multiplicative renormalization is needed. In the case of the vortex this involves a surprising cancellation. Next, the dependence of the Green's functions of the Wilson and 't Hooft operators on the nature of the vacuum is discussed. The cluster properties of the Green's functions are emphasized. It is seen that the vortex operator in a massive Abelian theory always has surface-like clustering. The form of Green's functions in terms of Feynman graphs is the same in Higgs and symmetric phases; the difference appears in the sum over all tadpole trees. Finally, systems having fields in the fundamental representation are considered. When these fields enter only weakly into the dynamics, a vortex-like operator is anticipated. Any such operator can no longer be local looplike, but must have commutators at long range. A U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint), is examined. When the fundamental field is weakly coupled, the expected phase transitions are found. When it is strongly coupled, the operator still appears to be a good order parameter, a discontinuous change in its behavior leads to a new phase transition. 18 figures

On the stability of the asymptotically free scalar field theories

Energy Technology Data Exchange (ETDEWEB)

Shalaby, A M. [Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha (Qatar); Physics Department, Faculty of Science, Mansoura University, Egypt. amshalab@qu.edu.qa (Egypt)

2015-03-30

Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.

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.)

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...

Canonical simulations with worldlines: An exploratory study in ϕ24 lattice field theory

Science.gov (United States)

Orasch, Oliver; Gattringer, Christof

2018-01-01

In this paper, we explore the perspectives for canonical simulations in the worldline formulation of a lattice field theory. Using the charged ϕ4 field in two dimensions as an example, we present the details of the canonical formulation based on worldlines and outline the algorithmic strategies for canonical worldline simulations. We discuss the steps for converting the data from the canonical approach to the grand canonical picture which we use for cross-checking our results. The canonical approach presented here can easily be generalized to other lattice field theories with a worldline representation.

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 ...

Field theory methods applied for the study of superconductivity in one-dimensional systems

International Nuclear Information System (INIS)

Martins, M.J.

1986-01-01

It is shown that the Froehlich's hamiltonian in one spatial dimension is identical to that of an exactly solvable field Theory. The spectrum of the theory is computed. A critical coupling is found above which the system becomes unstable, indicating a superconducting transition. It is also proposed and investigated a renormalizable relativistic field theory model in two space-time dimensions, with quartic self-interaction among N species of fermions, which undergoes dynamical generation of a superconducting gap and is asymptotically free. A finite temperature is introduced and, for N -> ∞ a critical value T c is found above which the gap vanishes. (author)

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

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.

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.

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)

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

Field theory approaches to new media practices

DEFF Research Database (Denmark)

Willig, Ida; Waltorp, Karen; Hartley, Jannie Møller

2015-01-01

could benefit particularly from Pierre Bourdieu’s research on cultural production. We introduce some of the literature that concerns digital media use and has been significant for field theory’s development in this context. We then present the four thematic articles in this issue and the articles......This special issue of MedieKultur specifically addresses new media practices and asks how field theory approaches can help us understand how culture is (prod)used via various digital platforms. In this article introducing the theme of the special issue, we argue that studies of new media practices...... outside the theme, which include two translations of classic texts within communications and media research. This introductory article concludes by encouraging media scholars to embark on additional studies within a field theory framework: This framework’s comprehensive theoretical basis and ideal...

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

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.)

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.)

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.

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

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.

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.

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.

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)

Noncommutative field theory and violation of translation invariance

International Nuclear Information System (INIS)

Bertolami, Orfeu; Guisado, Luis

2003-01-01

Noncommutative field theories with commutator of the coordinates of the form [x μ , x ν ] = i Λ μν ω x ω with nilpotent structure constants are studied and shown that a free quantum field theory is not affected. Invariance under translations is broken and the conservation of energy-momentum is violated, obeying a new law which is expressed by a Poincare-invariant equation. The resulting new kinematics is studied and applied to simple examples and to astrophysical puzzles, such as the observed violation of the GZK cutoff. The λΦ 4 quantum field theory is also considered in this context. In particular, self interaction terms violate the usual conservation of energy-momentum and, hence, the radiative correction to the propagator is altered. The correction to first order in λ is calculated. The usual UV divergent terms are still present, but a new type of term also emerges, which is IR divergent, violates momentum conservation and implies a correction to the dispersion relation. (author)

Einstein's theory of unified fields

CERN Document Server

Tonnelat, Marie Antoinette

2014-01-01

First published in1966, here is presented a comprehensive overview of one of the most elusive scientific speculations by the pre-eminent genius of the 20th century. The theory is viewed by some scientists with deep suspicion, by others with optimism, but all agree that it represents an extreme challenge. As the author herself affirms, this work is not intended to be a complete treatise or 'didactic exposition' of the theory of unified fields, but rather a tool for further study, both by students and professional physicists. Dealing with all the major areas of research whic

Fluctuation and dissipation in nonequilibrium quantum field theory

International Nuclear Information System (INIS)

Ramos, Rudnei O.

1994-01-01

The nonequilibrium dynamics of a scalar field is studied using perturbation theory and a real time finite temperature formulation. The evolution equation for the scalar field is explicitly obtained, and terms responsible for noise (fluctuations) and dissipation are identified and studied in the high temperature limit. (author)

Lattice formulation of a two-dimensional topological field theory

International Nuclear Information System (INIS)

Ohta, Kazutoshi; Takimi, Tomohisa

2007-01-01

We investigate an integrable property and the observables of 2-dimensional N=(4,4) topological field theory defined on a discrete lattice by using the 'orbifolding' and 'deconstruction' methods. We show that our lattice model is integrable and, for this reason, the partition function reduces to matrix integrals of scalar fields on the lattice sites. We elucidate meaningful differences between a discrete lattice and a differentiable manifold. This is important for studying topological quantities on a lattice. We also propose a new construction of N=(2,2) supersymmetric lattice theory, which is realized through a suitable truncation of scalar fields from the N=(4,4) theory. (author)

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.

Discussion of the duality in three dimensional quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Ma, Chen-Te, E-mail: yefgst@gmail.com

2017-05-10

We discuss the duality in three dimensional quantum field theory at infrared limit. The starting point is to use a conjecture of a duality between the free fermion and the interacting scalar field theories at the Wilson–Fisher fixed point. The conjecture is useful for deriving various dualities in three dimensions to obtain a duality web. The study is also interesting for understanding the dualities, or equivalence of different theories from the perspective of the renormalization group flow. We first discuss the “derivation” without losing the holonomy. Furthermore, we also derive these dualities from the mean-field study, and consider the extension of the conjecture or dualities at finite temperature.

Effective-field theory on the kinetic Ising model

International Nuclear Information System (INIS)

Shi Xiaoling; Wei Guozhu; Li Lin

2008-01-01

As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h 0 /ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT)

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.

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

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

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

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

Topological field theories and two-dimensional instantons

International Nuclear Information System (INIS)

Schaposnik, F.A.

1990-01-01

In this paper, the author discusses some topics related to the recently developed Topological Field Theories (TFTs). The first part is devoted to a discussion on how a TFT can be quantized using techniques which are well-known from the study of gauge theories. Then the author describes the results that we have obtained in collaboration with George Thompson in the study of a two-dimensional TFT related to the Abelian Higgs model

(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)

Lattice Field Theory with the Sign Problem and the Maximum Entropy Method

Directory of Open Access Journals (Sweden)

Masahiro Imachi

2007-02-01

Full Text Available Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the θ term. We reconsider this problem from the point of view of the maximum entropy method.

New ideas about unified field theory

International Nuclear Information System (INIS)

Gleiser, M.

1986-01-01

An outline of the physical concepts evolution is given from the ancient philosophers to the present time. With qualitative explanations about the meaning of the theories that is the milestones of these concepts evolution, it mentions the ideas which lead the studies to the conception of a unified field theory. Chronologically, it has brief information about the ideas of Laplace (mechanical determinism), Maxwell (the field concept), Einsten (the space-time structure), Heisenberg and Schroedinger (the quantum mechanics), Dirac (the relativistic quantum and the antiparticles), Gell-Mann (the quarks), Weinberg-Salam (Weak interactions and eletromagnetic unification), H. Georgi and S. Glashon (strong interactions plus Weinberg-Salam), Kaluza-Klein (a fifth space-time coordinate), and Zumino-Weiss (supersymmetry and supergravity). (G.D.F.) [pt

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

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.

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

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

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.

Classical open-string field theory: A∞-algebra, renormalization group and boundary states

International Nuclear Information System (INIS)

Nakatsu, Toshio

2002-01-01

We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. Classical open-string field theory in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of A ∞ -algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles

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 ...

A computational theory of visual receptive fields.

Science.gov (United States)

Lindeberg, Tony

2013-12-01

agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space-time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space-time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms.

Extensions of conformal symmetry in two-dimensional quantum field theory

International Nuclear Information System (INIS)

Schoutens, C.J.M.

1989-01-01

Conformal symmetry extensions in a two-dimensional quantum field theory are the main theme of the work presented in this thesis. After a brief exposition of the formalism for conformal field theory, the motivation for studying extended symmetries in conformal field theory is presented in some detail. Supersymmetric extensions of conformal symmetry are introduced. An overview of the algebraic superconformal symmetry is given. The relevance of higher-spin bosonic extensions of the Virasoro algebra in relation to the classification program for so-called rational conformal theories is explained. The construction of a large class of bosonic extended algebras, the so-called Casimir algebras, are presented. The representation theory of these algebras is discussed and a large class of new unitary models is identified. The superspace formalism for O(N)-extended superconformal quantum field theory is presented. It is shown that such theories exist for N ≤ 4. Special attention is paid to the case N = 4 and it is shown that the allowed central charges are c(n + ,n - ) = 6n + n - /(n + ,n - ), where n + and n - are positive integers. A different class of so(N)-extended superconformal algebras is analyzed. The representation theory is studied and it is established that certain free field theories provide realizations of the algebras with level S = 1. Finally the so-called BRST construction for extended conformal algebras is considered. A nilpotent BRST charge is constructed for a large class of algebras, which contains quadratically nonlinear algebras that fall outside the traditional class if finitely generated Lie (super)algebras. The results are especially relevant for the construction of string models based on extended conformal symmetry. (author). 118 refs.; 7 tabs

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

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.)

Perturbation Theory of the Cosmological Log-Density Field

DEFF Research Database (Denmark)

Wang, Xin; Neyrinck, Mark; Szapudi, István

2011-01-01

, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor...

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.

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

Long-range interactions in lattice field theory

International Nuclear Information System (INIS)

Rabin, J.M.

1981-06-01

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations

Long-range interactions in lattice field theory

Energy Technology Data Exchange (ETDEWEB)

Rabin, J.M.

1981-06-01

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.

Deformation of the cubic open string field theory

Energy Technology Data Exchange (ETDEWEB)

Lee, Taejin, E-mail: taejin@kangwon.ac.kr

2017-05-10

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

Deformation of the cubic open string field theory

International Nuclear Information System (INIS)

Lee, Taejin

2017-01-01

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

Deformation of the cubic open string field theory

Directory of Open Access Journals (Sweden)

Taejin Lee

2017-05-01

Full Text Available We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

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

International Nuclear Information System (INIS)

Bender, C.M.; Pinsky, S.; van de Sande, B.

1993-01-01

We study spontaneous symmetry breaking in (1+1)-dimensional φ 4 theory using the light-front formulation of field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero mode in the one-mode approximation. We find that spontaneous symmetry breaking occurs at λ critical =4π(3+ √3 )μ 2 , which is consistent with the value λ critical =54.27μ 2 obtained in the equal-time theory. We calculate the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the δ expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior for the broken phase

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

MHV, CSW and BCFW: field theory structures in string theory amplitudes

International Nuclear Information System (INIS)

Boels, Rutger; Larsen, Kasper Jens; Obers, Niels A.; Vonk, Marcel

2008-01-01

Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of α'-corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the α' 3 -correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.

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

Galois and simple current symmetries in conformal field theory

International Nuclear Information System (INIS)

Schweigert, C.

1995-01-01

In this thesis various aspects of rational field theories are studied. In part I explicit examples for N=2 superconformal field theories are constructed by means of the coset approach. By means of these models string vacua are constructed, and the massless spectra of the string compactifications based on these models are computed. The symmetry of the S matrix, which implements the modular transformation on the space of characters is the subject of Part II. The developed methods are applied to the fusion rings of WZW theories. (HSI)

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

Thanks to its impressive success in the second half of the 20th century, both in high-energy physics and in critical phenomena, quantum field theory has enjoyed an abundant literature. We therefore greet yet another book on this subject with caution: what can a monograph on quantum field theory bring now that is new, either conceptually or pedagogically? But when it is written by a physicist such as Bryce DeWitt, who has made his own contribution to the collection of field theory books with The Global Approach to Quantum Field Theory, all suspicion is naturally abandoned. DeWitt has made a formidable contribution to various areas of physics: general relativity, the interpretation of quantum mechanics, and most of all the quantization of non-Abelian gauge theories and quantum gravity. In addition, his pedagogical publications, especially the Les Houches schools of 1963 and 1983, have had a great impact on quantum field theory. We must begin by alerting the potential readers of this book that it cannot be compared to any other book in the field. This uniqueness applies to both the scientific content and the way the ideas are presented. For DeWitt, a central concept of field theory is that of 'space of histories'. For a field varphi{sup i} defined on a given spacetime M, the set of all varphi{sup i}(x) for all x in all charts of M defines its history. It is the space Phi of all possible histories (dynamically allowed or not) of the fields defined on M which is called the 'pace of histories' by DeWitt. If only bosonic fields are considered, the space of histories is an infinite-dimensional manifold and if fermionic fields are also present, it must be viewed as an infinite-dimensional supermanifold. The fields can then be regarded as coordinates on these structures, and the geometrical notions of differentiation, metric, connections, measure, as well as the geodesics which can be defined on it, are of fundamental importance in the development of the

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.

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)

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

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.

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.)

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

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

International Nuclear Information System (INIS)

Deviren, Bayram; Canko, Osman; Keskin, Mustafa

2010-01-01

Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tomé and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tomé and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h 0 ) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h 0 . (general)

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.

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)

An algebraic approach towards the classification of 2 dimensional conformal field theories

International Nuclear Information System (INIS)

Bouwknegt, P.G.

1988-01-01

This thesis treats an algebraic method for the construction of 2-dimensional conformal field theories. The method consists of the study of the representation theory of the Virasoro algebra and suitable extensions of this. The classification of 2-dimensional conformal field theories is translated into the classification of combinations of representations which satisfy certain consistence conditions (unitarity and modular invariance). For a certain class of 2-dimensional field theories, namely the one with central charge c = 1 from the theory of Kac-Moody algebra's. there exist indications, but as yet mainly hope, that this construction will finally lead to a classification of 2-dimensional conformal field theories. 182 refs.; 2 figs.; 26 tabs

Magnetic fields and density functional theory

Energy Technology Data Exchange (ETDEWEB)

Salsbury Jr., Freddie [Univ. of California, Berkeley, CA (United States)

1999-02-01

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.

Magnetic fields and density functional theory

International Nuclear Information System (INIS)

Salsbury, Freddie Jr.

1999-01-01

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules

Quantum Conformal Algebras and Closed Conformal Field Theory

CERN Document Server

Anselmi, D

1999-01-01

We investigate the quantum conformal algebras of N=2 and N=1 supersymmetric gauge theories. Phenomena occurring at strong coupling are analysed using the Nachtmann theorem and very general, model-independent, arguments. The results lead us to introduce a novel class of conformal field theories, identified by a closed quantum conformal algebra. We conjecture that they are the exact solution to the strongly coupled large-N_c limit of the open conformal field theories. We study the basic properties of closed conformal field theory and work out the operator product expansion of the conserved current multiplet T. The OPE structure is uniquely determined by two central charges, c and a. The multiplet T does not contain just the stress-tensor, but also R-currents and finite mass operators. For this reason, the ratio c/a is different from 1. On the other hand, an open algebra contains an infinite tower of non-conserved currents, organized in pairs and singlets with respect to renormalization mixing. T mixes with a se...

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

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.)

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.)

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

Quantum theory of relativistic charged particles in external fields

International Nuclear Information System (INIS)

Ruijsenaars, S.N.M.

1976-01-01

A study was made on external field theories in which the quantized field corresponds to relativistic elementary particles with non-zero rest mass. These particles are assumed to be charged, thus they have distinct antiparticles. The thesis consists of two parts. The first tries to accommodate the general features of theories of relativistic charged particles in external fields. Spin and dynamics in particular are not specified. In the second part, the results are applied to charged spin-1/2 and spin-0 particles, the dynamics of which are given by the Dirac resp. Klein-Gordon equation. The greater emphasis is on external fields which are rapidly decreasing, infinitely differentiable functions of space-time, but also considers time-independent fields. External fields, other than electromagnetic fields are also considered, e.g. scalar fields

Possible further subjects of study in the field of fusion plasma theory in Latvia

International Nuclear Information System (INIS)

Dumbrajs, O.

2004-01-01

Full text: First fusion plasma theory relevant studies in Latvia were related to edge localized modes (ELMs). This work has been carried out at the Institute of Solid Physics and is nearing successful completion. The next suggested topic 'Stochastisation of magnetic field lines and its impact on fusion plasma' is related to the theory of ergotic magnetic fields. The stochastisation of magnetic field lines is thought to play a major role in fast energy loss events from magnetically confined fusion plasma due to magnetohydrodynamic (MHD) modes. Classical examples are sawtooth crashes and disruptions. Here it is thought that stochastisation plays a role in the enhanced reconnection rate, which is often observed. More recently, this process has also been proposed as an explanation for the neoclassical tearing modes (NTM) phenomenon, which is repetitive rapid decrease of a neoclassical magnetic island due to its interaction with other MHD modes. The timescale for this phenomenon is clearly too fast to be explained by a conventional reconnection. The theoretical study of the onset of stochastisation will be illustrated for plasma parameters typical for the ASDEX Upgrade tokamak operated at the Max-Planc-Institute for Plasma Physics in Garching, Germany

Very special conformal field theories and their holographic duals

Science.gov (United States)

Nakayama, Yu

2018-03-01

Cohen and Glashow introduced the notion of very special relativity as viable space-time symmetry of elementary particle physics. As a natural generalization of their idea, we study the subgroup of the conformal group, dubbed very special conformal symmetry, which is an extension of the very special relativity. We classify all of them and construct field theory examples as well as holographic realization of the very special conformal field theories.

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.

Introduction to symmetry and supersymmetry in quantum field theory

International Nuclear Information System (INIS)

Lopuszanski, J.

1988-01-01

This is a set of lecture notes given by the author at the Universities of Gottingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one- semester course for graduate students in the field of mathematical physics and high energy physics. Contents: Introduction; Example of a Classical and Quantum Scalar Free Field Theory; Scene and Subject of the Drama. Axiom 1 and 2; Subject of the Drama; Principle of Relativity. Causality. Axiom 3, 4 and 5; Irreducibility of the Field Algebra and Scattering Theory. Axiom 6. Axiom O; Preliminaries about Physical Symmetries; Currents and Charges; Global Symmetries and Supersymmetries of the S - Matrix; Representations of the Super-Lie Algebra; The Case of Massless Particles; Fermionic Charges; Concluding Remarks

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

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

Preheating in an asymptotically safe quantum field theory

DEFF Research Database (Denmark)

Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert

2016-01-01

. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance...... fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F......We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J...

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)

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

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

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

BQP-completeness of scattering in scalar quantum field theory

Directory of Open Access Journals (Sweden)

Stephen P. Jordan

2018-01-01

Full Text Available Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1 dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

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)

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.

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)

The fixed point structure of lattice field theories

International Nuclear Information System (INIS)

Baier, R.; Reusch, H.J.; Lang, C.B.

1989-01-01

Monte-Carlo renormalization group methods allow to analyze lattice regularized quantum field theories. The properties of the quantized field theory in the continuum may be recovered at a critical point of the lattice model. This requires a study of the phase diagram and the renormalization flow structure of the coupling constants. As an example the authors discuss the results of a recent MCRG investigation of the SU(2) adjoint Higgs model, where they find evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β

Abelian Toda field theories on the noncommutative plane

Science.gov (United States)

Cabrera-Carnero, Iraida

2005-10-01

Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.

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...

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)

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.

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.

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

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...

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

Analytic properties of Feynman diagrams in quantum field theory

CERN Document Server

Todorov, I T

1971-01-01

Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with a

On osp(2|2) conformal field theories

International Nuclear Information System (INIS)

Ding Xiangmao; Gould, Mark D; Mewton, Courtney J; Zhang Yaozhong

2003-01-01

We study the conformal field theories corresponding to current superalgebras osp(2|2) (1) k and osp(2|2) (2) k . We construct the free field realizations, screen currents and primary fields of these current superalgebras at general level k. All the results for osp(2|2) (2) k are new, and the results for the primary fields of osp(2|2) (1) k also seem to be new. Our results are expected to be useful in the supersymmetric approach to Gaussian disordered systems such as the random bond Ising model and the Dirac model

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.)

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.

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.)

Nonperturbative approach to quantum field theories: phase transitions and confinement

International Nuclear Information System (INIS)

Yankielowicz, S.

1976-08-01

Lectures are given on a nonperturbative approach to quantum field theories. Phenomena are discussed for which the usual weak coupling perturbative approach in terms of Feynman diagrams is of no assistance. Properties associated with large distance behavior, i.e., phase transitions, low lying spectra, coherent excitations which are presumably built out of the long wave structure of the theory are described. These methods are important for the study of strong coupling field theories and the question of quarks confinement. 25 references

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

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.