Holographic applications of logarithmic conformal field theories

NARCIS (Netherlands)

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

2013-01-01

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

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.)

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.

Acoustic array systems theory, implementation, and application

CERN Document Server

Bai, Mingsian R; Benesty, Jacob

2013-01-01

Presents a unified framework of far-field and near-field array techniques for noise source identification and sound field visualization, from theory to application. Acoustic Array Systems: Theory, Implementation, and Application provides an overview of microphone array technology with applications in noise source identification and sound field visualization. In the comprehensive treatment of microphone arrays, the topics covered include an introduction to the theory, far-field and near-field array signal processing algorithms, practical implementations, and common applic

Higgs effective field theories. Systematics and applications

Energy Technology Data Exchange (ETDEWEB)

Krause, Claudius G.

2016-07-28

Researchers of the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) announced on July 4th, 2012, the observation of a new particle. The properties of the particle agree, within the relatively large experimental uncertainties, with the properties of the long-sought Higgs boson. Particle physicists around the globe are now wondering, ''Is it the Standard Model Higgs that we observe; or is it another particle with similar properties?'' We employ effective field theories (EFTs) for a general, model-independent description of the particle. We use a few, minimal assumptions - Standard Model (SM) particle content and a separation of scales to the new physics - which are supported by current experimental results. By construction, effective field theories describe a physical system only at a certain energy scale, in our case at the electroweak-scale v. Effects of new physics from a higher energy-scale, Λ, are described by modified interactions of the light particles. In this thesis, ''Higgs Effective Field Theories - Systematics and Applications'', we discuss effective field theories for the Higgs particle, which is not necessarily the Higgs of the Standard Model. In particular, we focus on a systematic and consistent expansion of the EFT. The systematics depends on the dynamics of the new physics. We distinguish two different consistent expansions. EFTs that describe decoupling new-physics effects and EFTs that describe non-decoupling new-physics effects. We briefly discuss the first case, the SM-EFT. The focus of this thesis, however, is on the non-decoupling EFTs. We argue that the loop expansion is the consistent expansion in the second case. We introduce the concept of chiral dimensions, equivalent to the loop expansion. Using the chiral dimensions, we expand the electroweak chiral Lagrangian up to next-to-leading order, O(f{sup 2}/Λ{sup 2})=O(1/16π{sup 2}). Further, we discuss how different

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

Applications of the absolute reaction rate theory to biological responses in electric and magnetic fields

International Nuclear Information System (INIS)

Brannen, J.P.; Wayland, J.R.

1976-01-01

This paper develops a theoretical foundation for the study of biological responses of electric and magnetic fields. The basis of the development is the absolute reaction rate theory and the effects of fields on reaction rates. A simple application to the response of Bacillus subtilis var niger in a microwave field is made. Potential areas of application are discussed

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

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

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

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

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.

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

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

Tensor categories and endomorphisms of von Neumann algebras with applications to quantum field theory

CERN Document Server

Bischoff, Marcel; Longo, Roberto; Rehren, Karl-Henning

2015-01-01

C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).

Comments on lightlike translations and applications in relativistic quantum field theory

International Nuclear Information System (INIS)

Driessler, W.

1975-01-01

In the algebraic framework of quantum field theory we consider one parameter subgroups of lightlike translations. After establishing a few preliminary properties we prove a certain cluster property and then exhibit the close connection between such subgroups and a class of type III factors. A few applications of this connection are also discussed. (orig.) [de

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.

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

Testing and application of the nuclear field theory: the nuclei 91Nb and 211Pb

International Nuclear Information System (INIS)

Liotta, R.J.; Silvestre-Brac, B.A.

1978-01-01

A method is presented for summing up the whole nuclear field theory series for the case of three particles outside a closed shell. The method is first illustrated within a simple model and then applied to the nucleus 91 Nb. In all the cases it is shown that the theory properly corrects the Pauli principle violations and the resulting overcompleteness of the basis. Finally, the application of the method in the analysis of the spectrum of 211 Pb gives a reasonable account of the experimental features. This last application also shows that the first-order perturbation method is in good agreement with the full application of the theory. (Auth.)

Cosmological applications of algebraic quantum field theory in curved spacetimes

CERN Document Server

Hack, Thomas-Paul

2016-01-01

This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.

Advanced number theory with applications

CERN Document Server

Mollin, Richard A

2009-01-01

Algebraic Number Theory and Quadratic Fields Algebraic Number Fields The Gaussian Field Euclidean Quadratic Fields Applications of Unique Factorization Ideals The Arithmetic of Ideals in Quadratic Fields Dedekind Domains Application to Factoring Binary Quadratic Forms Basics Composition and the Form Class Group Applications via Ambiguity Genus Representation Equivalence Modulo p Diophantine Approximation Algebraic and Transcendental Numbers Transcendence Minkowski's Convex Body Theorem Arithmetic Functions The Euler-Maclaurin Summation Formula Average Orders The Riemann zeta-functionIntroduction to p-Adic AnalysisSolving Modulo pn Introduction to Valuations Non-Archimedean vs. Archimedean Valuations Representation of p-Adic NumbersDirichlet: Characters, Density, and Primes in Progression Dirichlet Characters Dirichlet's L-Function and Theorem Dirichlet DensityApplications to Diophantine Equations Lucas-Lehmer Theory Generalized Ramanujan-Nagell Equations Bachet's Equation The Fermat Equation Catalan and the A...

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 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.

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)

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...

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)

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.

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.

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

International Nuclear Information System (INIS)

Bruneton, Jean-Philippe

2007-01-01

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

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

Mean-field theory of nuclear structure and dynamics

International Nuclear Information System (INIS)

Negele, J.W.

1982-01-01

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

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

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.

Introductory lectures on quantum field theory

International Nuclear Information System (INIS)

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

2011-01-01

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

An application of information theory to stochastic classical gravitational fields

Science.gov (United States)

Angulo, J.; Angulo, J. C.; Angulo, J. M.

2018-06-01

The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.

Unitary field theories

International Nuclear Information System (INIS)

Bergmann, P.G.

1980-01-01

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

Nonlocal quantum field theory and stochastic quantum mechanics

International Nuclear Information System (INIS)

Namsrai, K.

1986-01-01

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

Finite fields and applications

CERN Document Server

Mullen, Gary L

2007-01-01

This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications. The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields. Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises rel...

Wilson lines in quantum field theory

Energy Technology Data Exchange (ETDEWEB)

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

2014-07-01

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

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.

Advances in dynamic and mean field games theory, applications, and numerical methods

CERN Document Server

Viscolani, Bruno

2017-01-01

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinar...

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

Finite spatial volume approach to finite temperature field theory

International Nuclear Information System (INIS)

Weiss, Nathan

1981-01-01

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

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.

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.)

String field theory

International Nuclear Information System (INIS)

Kaku, M.

1987-01-01

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

[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

String theory or field theory?

International Nuclear Information System (INIS)

Marshakov, Andrei V

2002-01-01

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

Geophysical Field Theory

International Nuclear Information System (INIS)

Eloranta, E.

2003-11-01

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

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

Quantum field theory

International Nuclear Information System (INIS)

Ryder, L.H.

1985-01-01

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

Classical field theory

CERN Document Server

Franklin, Joel

2017-01-01

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

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 ...

Holographic effective field theories

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-28

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

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.)

Conformal field theory and 2D critical phenomena. Part 1

International Nuclear Information System (INIS)

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

1989-01-01

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

Lectures on classical and quantum theory of fields

CERN Document Server

Arodz, Henryk

2017-01-01

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

Applications of Canonical transformations and nontrivial vacuum solutions to flavor mixing and critical phenomena in quantum field theory

International Nuclear Information System (INIS)

Mishchenko, Yuriy

2004-01-01

MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati

Applications of Canonical transformations and nontrivial vacuum solutions to flavor mixing and critical phenomena in quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Mishchenko, Yuriy [North Carolina State Univ., Raleigh, NC (United States)

2004-12-01

MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati

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

The use of random walk in field theory

International Nuclear Information System (INIS)

Brydges, D.

1984-01-01

Ferromagnetic spin systems and gauge theories where the gauge group is topologically a sphere, e.g. Z 2 , U(1) and SU(2) are related to the theory of random walk and random surfaces respectively. I survey some applications of this theme to the phi 4 field theories. (orig.)

Dynamic random walks theory and applications

CERN Document Server

Guillotin-Plantard, Nadine

2006-01-01

The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!).· New probabilistic model, new results in probability theory· Original applications in computer science· Applications in mathematical physics· Applications in finance

Differential algebras in field theory

International Nuclear Information System (INIS)

Stora, R.

1988-01-01

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

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

Nonequilibrium molecular dynamics theory, algorithms and applications

CERN Document Server

Todd, Billy D

2017-01-01

Written by two specialists with over twenty-five years of experience in the field, this valuable text presents a wide range of topics within the growing field of nonequilibrium molecular dynamics (NEMD). It introduces theories which are fundamental to the field - namely, nonequilibrium statistical mechanics and nonequilibrium thermodynamics - and provides state-of-the-art algorithms and advice for designing reliable NEMD code, as well as examining applications for both atomic and molecular fluids. It discusses homogenous and inhomogenous flows and pays considerable attention to highly confined fluids, such as nanofluidics. In addition to statistical mechanics and thermodynamics, the book covers the themes of temperature and thermodynamic fluxes and their computation, the theory and algorithms for homogenous shear and elongational flows, response theory and its applications, heat and mass transport algorithms, applications in molecular rheology, highly confined fluids (nanofluidics), the phenomenon of slip and...

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

On the algebraic theory of kink sectors: Application to quantum field theory models and collision theory

International Nuclear Information System (INIS)

Schlingemann, D.

1996-10-01

Several two dimensional quantum field theory models have more than one vacuum state. An investigation of super selection sectors in two dimensions from an axiomatic point of view suggests that there should be also states, called soliton or kink states, which interpolate different vacua. Familiar quantum field theory models, for which the existence of kink states have been proven, are the Sine-Gordon and the φ 4 2 -model. In order to establish the existence of kink states for a larger class of models, we investigate the following question: Which are sufficient conditions a pair of vacuum states has to fulfill, such that an interpolating kink state can be constructed? We discuss the problem in the framework of algebraic quantum field theory which includes, for example, the P(φ) 2 -models. We identify a large class of vacuum states, including the vacua of the P(φ) 2 -models, the Yukawa 2 -like models and special types of Wess-Zumino models, for which there is a natural way to construct an interpolating kink state. In two space-time dimensions, massive particle states are kink states. We apply the Haag-Ruelle collision theory to kink sectors in order to analyze the asymptotic scattering states. We show that for special configurations of n kinks the scattering states describe n freely moving non interacting particles. (orig.)

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)

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

CERN Document Server

Bars, Itzhak

2010-01-01

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

Wavelet theory and its applications

Energy Technology Data Exchange (ETDEWEB)

Faber, V.; Bradley, JJ.; Brislawn, C.; Dougherty, R.; Hawrylycz, M.

1996-07-01

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). We investigated the theory of wavelet transforms and their relation to Laboratory applications. The investigators have had considerable success in the past applying wavelet techniques to the numerical solution of optimal control problems for distributed- parameter systems, nonlinear signal estimation, and compression of digital imagery and multidimensional data. Wavelet theory involves ideas from the fields of harmonic analysis, numerical linear algebra, digital signal processing, approximation theory, and numerical analysis, and the new computational tools arising from wavelet theory are proving to be ideal for many Laboratory applications. 10 refs.

Generalized locally Toeplitz sequences theory and applications

CERN Document Server

Garoni, Carlo

2017-01-01

Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related applications in the unidimensional setting, while the second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications. This book systematically develops the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications, with a particular focus on the numerical discretization of differential equations (DEs). It is the first book to address the relatively new field of GLT sequences, which occur in numerous scientific applications and are especially dominant in the context of DE discretizations. Written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research, it is also of interest to those working in the fields of...

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

Energy Technology Data Exchange (ETDEWEB)

Scheck, Florian

2018-04-01

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

Effective field theory: A modern approach to anomalous couplings

International Nuclear Information System (INIS)

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

2013-01-01

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

Effective quantum field theories

International Nuclear Information System (INIS)

Georgi, H.M.

1993-01-01

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

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.

Classical field theory on electrodynamics, non-abelian gauge theories and gravitation

CERN Document Server

Scheck, Florian

2018-01-01

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

From Landau's hydrodynamical model to field theory model to field theory models of multiparticle production: a tribute to Peter

International Nuclear Information System (INIS)

Cooper, F.

1996-01-01

We review the assumptions and domain of applicability of Landau's Hydrodynamical Model. By considering two models of particle production, pair production from strong electric fields and particle production in the linear σ model, we demonstrate that many of Landau's ideas are verified in explicit field theory calculations

Classification of networks of automata by dynamical mean field theory

International Nuclear Information System (INIS)

Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.

1990-01-01

Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)

Catastrophe theory and its application status in mechanical engineering

Directory of Open Access Journals (Sweden)

Jinge LIU

Full Text Available Catastrophe theory is a kind of mathematical method which aims to apply and interpret the discontinuous phenomenon. Since its emergence, it has been widely used to explain a variety of emergent phenomena in the fields of natural science, social science, management science and some other science and technology fields. Firstly, this paper introduces the theory of catastrophe in several aspects, such as its generation, radical principle, basic characteristics and development. Secondly, it summarizes the main applications of catastrophe theory in the field of mechanical engineering, focusing on the research progress of catastrophe theory in revealing catastrophe of rotor vibration state, analyzing friction and wear failure, predicting metal fracture, and so on. Finally, it advises that later development of catastrophe theory should pay more attention to the combination of itself with other traditional nonlinear theories and methods. This paper provides a beneficial reference to guide the application of catastrophe theory in mechanical engineering and related fields for later research.

Field theory and strings

International Nuclear Information System (INIS)

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

1987-01-01

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

Effective field theory for triaxially deformed nuclei

Energy Technology Data Exchange (ETDEWEB)

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

2017-10-15

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

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

Workshop on Thermal Field Theory to Neural Networks

CERN Document Server

Veneziano, Gabriele; Aurenche, Patrick

1996-01-01

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

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

Astrophysical data analysis with information field theory

International Nuclear Information System (INIS)

Enßlin, Torsten

2014-01-01

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

Astrophysical data analysis with information field theory

Science.gov (United States)

Enßlin, Torsten

2014-12-01

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

Astrophysical data analysis with information field theory

Energy Technology Data Exchange (ETDEWEB)

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

2014-12-05

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

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 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)

Studies in quantum field theory

International Nuclear Information System (INIS)

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

1982-01-01

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

Implementation of visual programming methods for numerical techniques used in electromagnetic field theory

Directory of Open Access Journals (Sweden)

Metin Varan

2017-08-01

Full Text Available Field theory is one of the two sub-field theories in electrical and electronics engineering that for creates difficulties for undergraduate students. In undergraduate period, field theory has been taught under the theory of electromagnetic fields by which describes using partial differential equations and integral methods. Analytical methods for solution of field problems on the basis of a mathematical model may result the understanding difficulties for undergraduate students due to their mathematical and physical infrastructure. The analytical methods which can be applied in simple model lose their applicability to more complex models. In this case, the numerical methods are used to solve more complex equations. In this study, by preparing some field theory‘s web-based graphical user interface numerical methods of applications it has been aimed to increase learning levels of field theory problems for undergraduate and graduate students while taking in mind their computer programming capabilities.

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

Directory of Open Access Journals (Sweden)

Stefan Hollands

2009-09-01

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

Correcting Improper Uses of Perspectives, Pronouns, and Dualities in Wilberian Integral Theory: An Application of Holarchical Field Theory

Directory of Open Access Journals (Sweden)

Kevin J. Bowman

2014-03-01

Full Text Available This article uses my pre-existing extension of Wilberian metatheory, holarchical field theory, to diagnose and work towards overcoming the confusion within attempts to analyze action, events, and communication using Ken Wilber’s AQAL model. In holarchical field theory, holarchical fields become the fundamental component of reality. These fields comprise 1 holons in relation to one another and to their potential, and 2 their interpenetrating forces engaged by their interactions. In light of the theory, problems in the Wilberian literature have included inconsistent uses of certain dualities (subject-object, interior-exterior, and inside-outside as well as person perspectives and pronouns. Previous attempts to overcome these issues without precise diagnoses suffer from a conflation of the dual definitions of the subjective-objective duality, one a philosophical definition, the other grammatical. State versus action language is classified within the dualities of holarchical field theory.

Chemical Thermodynamics and Information Theory with Applications

CERN Document Server

Graham, Daniel J

2011-01-01

Thermodynamics and information touch theory every facet of chemistry. However, the physical chemistry curriculum digested by students worldwide is still heavily skewed toward heat/work principles established more than a century ago. Rectifying this situation, Chemical Thermodynamics and Information Theory with Applications explores applications drawn from the intersection of thermodynamics and information theory--two mature and far-reaching fields. In an approach that intertwines information science and chemistry, this book covers: The informational aspects of thermodynamic state equations The

Informetrics theory, methods and applications

CERN Document Server

Qiu, Junping; Yang, Siluo; Dong, Ke

2017-01-01

This book provides an accessible introduction to the history, theory and techniques of informetrics. Divided into 14 chapters, it develops the content system of informetrics from the theory, methods and applications; systematically analyzes the six basic laws and the theory basis of informetrics and presents quantitative analysis methods such as citation analysis and computer-aided analysis. It also discusses applications in information resource management, information and library science, science of science, scientific evaluation and the forecast field. Lastly, it describes a new development in informetrics- webometrics. Providing a comprehensive overview of the complex issues in today's environment, this book is a valuable resource for all researchers, students and practitioners in library and information science.

The general theory of quantized fields in the 1950s

International Nuclear Information System (INIS)

Wightman, A.S.

1989-01-01

This review describes developments in theoretical particle physics in the 1950s which were important in the race to develop a putative general theory of quantized fields, especially ideas that offered a mathematically rigorous theory. Basic theoretical concepts then available included the Hamiltonian formulation of quantum dynamics, canonical quantization, perturbative renormalization theory and the theory of distributions. Following a description of various important theoretical contributions of this era, the review ends with a summary of the most important contributions of axiomatic field theory to concrete physics applications. (UK)

QCD Effective Field Theories for Heavy Quarkonium

International Nuclear Information System (INIS)

Brambilla, Nora

2006-01-01

QCD nonrelativistic effective field theories (NREFT) are the modern and most suitable frame to describe heavy quarkonium properties. Here I summarize few relevant concepts and some of the interesting physical applications (spectrum, decays, production) of NREFT

Structural aspects of quantum field theory and noncommutative geometry

CERN Document Server

Grensing, Gerhard

2013-01-01

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

Quantum groups, quantum categories and quantum field theory

CERN Document Server

Fröhlich, Jürg

1993-01-01

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

Twisted conformal field theories and Morita equivalence

Energy Technology Data Exchange (ETDEWEB)

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

2009-04-01

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

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

International Nuclear Information System (INIS)

Chowdhury, A.R.; Roy, T.

1980-01-01

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

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

CERN Document Server

Recknagel, Andreas

2013-01-01

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

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

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.)

OPE convergence in non-relativistic conformal field theories

Energy Technology Data Exchange (ETDEWEB)

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

2015-12-09

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

Applicability of self-consistent mean-field theory

International Nuclear Information System (INIS)

Guo Lu; Sakata, Fumihiko; Zhao Enguang

2005-01-01

Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case

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.)

Shell-like structures advanced theories and applications

CERN Document Server

Eremeyev, Victor

2017-01-01

The book presents mathematical and mechanical aspects of the theory of plates and shells, applications in civil, aero-space and mechanical engineering, as well in other areas. The focus relates to the following problems: • comprehensive review of the most popular theories of plates and shells, • relations between three-dimensional theories and two-dimensional ones, • presentation of recently developed new refined plates and shells theories (for example, the micropolar theory or gradient-type theories), • modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc., • applications in modeling of non-classical objects like, for example, nanostructures, • presentation of actual numerical tools based on the finite element approach.

Thermal field theory in a layer: Applications of thermal field theory methods to the propagation of photons in a two-dimensional electron sheet

International Nuclear Information System (INIS)

Nieves, Jose F.

2010-01-01

We apply the thermal field theory methods to study the propagation of photons in a plasma layer, that is a plasma in which the electrons are confined to a two-dimensional plane sheet. We calculate the photon self-energy and determine the appropriate expression for the photon propagator in such a medium, from which the properties of the propagating modes are obtained. The formulas for the photon dispersion relations and polarization vectors are derived explicitly in some detail for some simple cases of the thermal distributions of the charged particle gas, and appropriate formulas that are applicable in more general situations are also given.

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.

Conformal dimension theory and application

CERN Document Server

Mackay, John M

2010-01-01

Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed ...

Selected Topics in Light Front Field Theory and Applications to the High Energy Phenomena

Science.gov (United States)

Kundu, Rajen

1999-10-01

In this thesis, we have presented some of the aspects of light-front (LF) field theory through their successful application in the Deep Inelastic Scattering (DIS). We have developed a LFQCD Hamiltonian description of the DIS structure functions starting from Bjorken-Johnson-Low limit of virtual forward Compton scattering amplitude and using LF current commutators. We worked in the LF gauge A^+=0 and used the old-fashioned LFQCD perturbation theory in our calculations. The importance of our work are summarized below. Our approach shares the intution of parton model and addresses directly the structure functions, which are experimental objects, instead of its moments as in OPE method. Moreover, it can potentially incorporate the non-perturbative contents of the structure functions as we have demonstrated by introducing a new factorization scheme. In the context of nucleonic helicity structure, the well known gauge fixed LF helicity operator is shown to provide consistent physical information and helps us defining new relevant structure functions. The anomalous dimensions relevant for the Q^2-evolution of such structure functions are calculated. Our study is important in establishing the equivalance of LF field theory and the usual equal-time one through perturbative calculations of the dressed parton structure functions reproducing the well known results. Also the importance of Gallilean boost symmetry in understanding the correctness of any higher order calculation using (x^+)-ordered LFQCD perturbation theory are emphasized.

Quantum field theory and the internal states of elementary particles

CSIR Research Space (South Africa)

Greben, JM

2011-01-01

Full Text Available A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent fields...

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)

Constrained variational calculus for higher order classical field theories

Energy Technology Data Exchange (ETDEWEB)

Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)

2010-11-12

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Constrained variational calculus for higher order classical field theories

International Nuclear Information System (INIS)

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

2010-01-01

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

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)

Proceedings of the 5. Jorge Andre Swieca Summer School Field Theory and Particle Physics

International Nuclear Information System (INIS)

Eboli, O.J.P.; Gomes, M.; Santoro, A.

1989-01-01

Lectures on quantum field theories and particle physics are presented. The part of quantum field theories contains: constrained dynamics; Schroedinger representation in field theory; application of this representation to quantum fields in a Robertson-Walker space-time; Berry connection; problem of construction and classification of conformal field theories; lattice models; two-dimensional S matrices and conformal field theory for unifying perspective of Yang-Baxter algebras; parasupersymmetric quantum mechanics; introduction to string field theory; three dimensional gravity and two-dimensional parafermionic model. The part of particle physics contains: collider physics; strong interactions and use of strings in strong interactions. (M.C.K.)

The Global Approach to Quantum Field Theory

Energy Technology Data Exchange (ETDEWEB)

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

2003-12-12

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

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

Causality Constraints in Conformal Field Theory

CERN Multimedia

CERN. Geneva

2015-01-01

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

Causality constraints in conformal field theory

Energy Technology Data Exchange (ETDEWEB)

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

2016-05-17

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

Bound state quantum field theory application to atoms and ions

CERN Document Server

Sapirstein, Jonathan

2019-01-01

Two aspects of the book should appeal to a wide audience. One aspect would be the comprehensive coverage on the latest updates and developments this book provides, besides Bethe and Salpeter's handbook on hydrogen and helium, which is still widely regarded as useful. The other aspect would be that a major part of the book uses “effective field theory”, a way of including quantum electrodynamics (QED) that starts with the familiar Schrödinger equation, and then adds perturbing operators derived in a rather simple manner that incorporates QED. Effective field theory is used in a number of fields including particle physics and nuclear physics, and readership is targeted at these communities too.Additionally, students using this book in conjunction with Peskin's textbook could learn to carry out fairly sophisticated calculations in QED in order to learn the technique, as this book comes with practical calculations.Also included is a very clear exposition of the Bethe–Salpeter equation, which is simply either ...

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.

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.

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

Advanced electromagnetism foundations, theory and applications

CERN Document Server

Barrett, Terence W

1995-01-01

Advanced Electromagnetism: Foundations, Theory and Applications treats what is conventionally called electromagnetism or Maxwell's theory within the context of gauge theory or Yang-Mills theory. A major theme of this book is that fields are not stand-alone entities but are defined by their boundary conditions. The book has practical relevance to efficient antenna design, the understanding of forces and stresses in high energy pulses, ring laser gyros, high speed computer logic elements, efficient transfer of power, parametric conversion, and many other devices and systems. Conventional electro

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.)

Theory of gravitational-inertial field of universe. 1

International Nuclear Information System (INIS)

Davtyan, O.K.

1978-01-01

A generalization of the real world tensor by the introduction of a inertial field tensor is proposed. On the basis of variational equations a system of more general covariant equations of the gravitational-inertial field is obtained. In the Einstein approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems in the general theory of relativity by means of the new equations gives the same results as the solution by means of Einstein's equations. However, application of these equations to the cosmologic problem gives a result different from that obtained by Friedmann's theory. In particular, the solution gives the Hubble law as the law of motion of a free body in the inertial field - in contrast to Galileo-Newton's law. (author)

Hydrodynamics, fields and constants in gravitational theory

International Nuclear Information System (INIS)

Stanyukovich, K.P.; Mel'nikov, V.N.

1983-01-01

Results of original inveatigations into problems of standard gravitation theory and its generalizations are presented. The main attention is paid to the application of methods of continuous media techniques in the gravitation theory; to the specification of the gravitation role in phenomena of macro- and microworld, accurate solutions in the case, when the medium is the matter, assigned by hydrodynamic energy-momentum tensor; and to accurate solutions for the case when the medium is the field. GRT generalizations are analyzed, such as the new cosmologic hypothesis which is based on the gravitation vacuum theory. Investigations are performed into the quantization of cosmological models, effects of spontaneous symmetry violation and particle production in cosmology. Graeity theory with fundamental Higgs field is suggested in the framework of which in the atomic unit number one can explain possible variations of the effective gravitational bonds, and in the gravitation bond, variations of masses of all particles

About Applications of the Fixed Point Theory

Directory of Open Access Journals (Sweden)

Bucur Amelia

2017-06-01

Full Text Available The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

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.)

Localization and diagonalization. A review of functional integral techniques for low-dimensional gauge theories and topological field theories

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1995-01-01

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory. (author). 83 refs

Rheology v.3 theory and applications

CERN Document Server

Eirich, Frederick

1960-01-01

Rheology: Theory and Applications, Volume 3 is a collection of articles contributed by experts in the field of rheology - the science of deformation and flow. This volume is composed of specialized chapters on the application of normal coordinate analysis to the theory of high polymers; principles of rheometry; and the rheology of cross-linked plastics, poly electrolytes, latexes, inks, pastes, and clay. Also included are a series of technological articles on lubrication, spinning, molding, extrusion, and adhesion and a survey of the general features of industrial rheology. Materials scientist

Regularity theory for mean-field game systems

CERN Document Server

Gomes, Diogo A; Voskanyan, Vardan

2016-01-01

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Regularity Theory for Mean-Field Game Systems

KAUST Repository

Gomes, Diogo A.

2016-09-14

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Regularity Theory for Mean-Field Game Systems

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.

2016-01-01

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

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 Mie Theory Basics and Applications

CERN Document Server

Wriedt, Thomas

2012-01-01

This book presents in a concise way the Mie theory and its current applications. It begins with an overview of current theories, computational methods, experimental techniques, and applications of optics of small particles. There is also some biographic information on Gustav Mie, who published his famous paper on the colour of Gold colloids in 1908. The Mie solution for the light scattering of small spherical particles set the basis for more advanced scattering theories and today there are many methods to calculate light scattering and absorption for practically any shape and composition of particles. The optics of small particles is of interest in industrial, atmospheric, astronomic and other research. The book covers the latest developments in divers fields in scattering theory such as plasmon resonance, multiple scattering and optical force.

Elements of the theory of Markov processes and their applications

CERN Document Server

Bharucha-Reid, A T

2010-01-01

This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.

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.)

Quantum field theory of fluids.

Science.gov (United States)

Gripaios, Ben; Sutherland, Dave

2015-02-20

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

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)

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

Quantum field theory in 2+1 dimensions

International Nuclear Information System (INIS)

Marino, E.C.

1998-01-01

An introductory review is made of many outstanding features of Quantum Field Theory formulated in three-dimensional spacetime. These include topological properties, the Huygens Principle, the Coulomb potential, topological excitations like vortices and skyrmions, dynamical mass generation, fractional spin and statistics, duality nd bosonization. Theories including the Maxwell-Chern-Simons, Abelian Higgs and C P 1 -Nonlinear Sigma Model are used to illustrate the different features. Applications to High-T c Superconductivity and to the Quantum Hall Effect are also presented. (author)

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

Group theory and lattice gauge fields

International Nuclear Information System (INIS)

Creutz, M.

1988-09-01

Lattice gauge theory, formulated in terms of invariant integrals over group elements on lattice bonds, benefits from many group theoretical notions. Gauge invariance provides an enormous symmetry and powerful constraints on expectation values. Strong coupling expansions require invariant integrals over polynomials in group elements, all of which can be evaluated by symmetry considerations. Numerical simulations involve random walks over the group. These walks automatically generate the invariant group measure, avoiding explicit parameterization. A recently proposed overrelaxation algorithm is particularly efficient at exploring the group manifold. These and other applications of group theory to lattice gauge fields are reviewed in this talk. 17 refs

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)

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

Effective field theory of cosmological perturbations

International Nuclear Information System (INIS)

Piazza, Federico; Vernizzi, Filippo

2013-01-01

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

Effective field theory of cosmological perturbations

Science.gov (United States)

Piazza, Federico; Vernizzi, Filippo

2013-11-01

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

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

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)

[Studies in quantum field theory

International Nuclear Information System (INIS)

1990-01-01

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

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

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.)

Current topics in summability theory and applications

CERN Document Server

Rhoades, Billy

2016-01-01

This book discusses recent developments in and contemporary research on summability theory, including general summability methods, direct theorems on summability, absolute and strong summability, special methods of summability, functional analytic methods in summability, and related topics and applications. All contributing authors are eminent scientists, researchers and scholars in their respective fields, and hail from around the world. The book can be used as a textbook for graduate and senior undergraduate students, and as a valuable reference guide for researchers and practitioners in the fields of summability theory and functional analysis. Summability theory is generally used in analysis and applied mathematics. It plays an important part in the engineering sciences, and various aspects of the theory have long since been studied by researchers all over the world. .

The renormalized action principle in quantum field theory

International Nuclear Information System (INIS)

Balasin, H.

1990-03-01

The renormalized action principle holds a central position in field theory, since it offers a variety of applications. The main concern of this work is the proof of the action principle within the so-called BPHZ-scheme of renormalization. Following the classical proof given by Lam and Lowenstein, some loopholes are detected and closed. The second part of the work deals with the application of the action principle to pure Yang-Mills-theories within the axial gauge (n 2 ≠ 0). With the help of the action principle we investigate the decoupling of the Faddeev-Popov-ghost-fields from the gauge field. The consistency of this procedure, suggested by three-graph approximation, is proven to survive quantization. Finally we deal with the breaking of Lorentz-symmetry caused by the presence of the gauge-direction n. Using BRST-like techniques and the semi-simplicity of the Lorentz-group, it is shown that no new breakings arise from quantization. Again the main step of the proof is provided by the action principle. (Author, shortened by G.Q.)

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)

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)

Logarithmic conformal field theory

Science.gov (United States)

Gainutdinov, Azat; Ridout, David; Runkel, Ingo

2013-12-01

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

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.)

Scattering of decuplet baryons in chiral effective field theory

Energy Technology Data Exchange (ETDEWEB)

Haidenbauer, J. [Institut fuer Kernphysik, Institute for Advanced Simulation and Juelich Center for Hadron Physics, Juelich (Germany); Petschauer, S.; Kaiser, N.; Weise, W. [Technische Universitaet Muenchen, Physik Department, Garching (Germany); Meissner, Ulf G. [Institut fuer Kernphysik, Institute for Advanced Simulation and Juelich Center for Hadron Physics, Juelich (Germany); Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany)

2017-11-15

A formalism for treating the scattering of decuplet baryons in chiral effective field theory is developed. The minimal Lagrangian and potentials in leading-order SU(3) chiral effective field theory for the interactions of octet baryons (B) and decuplet baryons (D) for the transitions BB → BB, BB <-> DB, DB → DB, BB <-> DD, DB <-> DD, and DD → DD are provided. As an application of the formalism we compare with results from lattice QCD simulations for ΩΩ and NΩ scattering. Implications of our results pertinent to the quest for dibaryons are discussed. (orig.)

The application of mean field theory to image motion estimation.

Science.gov (United States)

Zhang, J; Hanauer, G G

1995-01-01

Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.

The application of Regge calculus to quantum gravity and quantum field theory in a curved background

International Nuclear Information System (INIS)

Warner, N.P.

1982-01-01

The application of Regge calculus to quantum gravity and quantum field theory in a curved background is discussed. A discrete form of exterior differential calculus is developed, and this is used to obtain Laplacians for p-forms on the Regge manifold. To assess the accuracy of these approximations, the eigenvalues of the discrete Laplacians were calculated for the regular tesselations of S 2 and S 3 . The results indicate that the methods obtained in this paper may be used in curved space-times with an accuracy comparing with that obtained in lattice gauge theories on a flat background. It also becomes evident that Regge calculus provides particularly suitable lattices for Monte-Carlo techniques. (author)

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...

Krichever-Novikov type algebras theory and applications

CERN Document Server

Schlichenmaier, Martin

2014-01-01

Krichever and Novikov introduced certain classes of infinite dimensionalLie algebrasto extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them toa more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin are

Noncommutative field theory

International Nuclear Information System (INIS)

Douglas, Michael R.; Nekrasov, Nikita A.

2001-01-01

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

Supergravity and Yang-Mills theories as generalized topological fields with constraints

International Nuclear Information System (INIS)

Ling Yi; Tung Rohsuan; Guo Hanying

2004-01-01

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand

Exclusion Statistics in Conformal Field Theory Spectra

International Nuclear Information System (INIS)

Schoutens, K.

1997-01-01

We propose a new method for investigating the exclusion statistics of quasiparticles in conformal field theory (CFT) spectra. The method leads to one-particle distribution functions, which generalize the Fermi-Dirac distribution. For the simplest SU(n) invariant CFTs we find a generalization of Gentile parafermions, and we obtain new distributions for the simplest Z N -invariant CFTs. In special examples, our approach reproduces distributions based on 'fractional exclusion statistics' in the sense of Haldane. We comment on applications to fractional quantum Hall effect edge theories. copyright 1997 The American Physical Society

Coarse grainings and irreversibility in quantum field theory

International Nuclear Information System (INIS)

Anastopoulos, C.

1997-01-01

In this paper we are interested in studying coarse graining in field theories using the language of quantum open systems. Motivated by the ideas of Hu and Calzetta on correlation histories we employ the Zwanzig projection technique to obtain evolution equations for relevant observables in self-interacting scalar field theories. Our coarse-graining operation consists in concentrating solely on the evolution of the correlation functions of degree less than n, a treatment which corresponds to the familiar truncation of the BBKGY hierarchy at the nth level. We derive the equations governing the evolution of mean-field and two-point functions thus identifying the terms corresponding to dissipation and noise. We discuss possible applications of our formalism, the emergence of classical behavior, and the connection to the decoherent histories framework. copyright 1997 The American Physical Society

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.)

Two applications of Berry's phase in fermionic field theory

International Nuclear Information System (INIS)

Goff, W.E.

1989-01-01

When quantized fermions are coupled to a background field, nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superfluid 3 He-A. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the 3 He-A equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero groundstate Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a Wess-Zumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a ground-state phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work

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

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.)

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.)

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)

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)

Full nuclear field theory treatment of two-particle-one-hole-excitations

International Nuclear Information System (INIS)

Silvestre-Brac, B.; Liotta, R.J.

1981-01-01

The nuclear field theory series is summed up to all orders of perturbation theory including only Tamm-Dancoff vertices for the case of two-particle-one-hole-excitations. It is found that the theory gives the same results as those provided by the shell-model method, but only if all possible basis states are included in the formalism. Applicability of the theory is discussed in a simple model

Application of the random field theory in PET imaging - injection dose optimization

Czech Academy of Sciences Publication Activity Database

Dvořák, Jiří; Boldyš, Jiří; Skopalová, M.; Bělohlávek, O.

2013-01-01

Roč. 49, č. 2 (2013), s. 280-300 ISSN 0023-5954 R&D Projects: GA MŠk 1M0572 Institutional support: RVO:67985556 Keywords : random field theory * Euler characteristic * PET imaging * PET image quality Subject RIV: BD - Theory of Information Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/ZOI/boldys-0397176.pdf

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

Effective-field theories for heavy quarkonium

International Nuclear Information System (INIS)

Brambilla, Nora; Pineda, Antonio; Soto, Joan; Vairo, Antonio

2005-01-01

This article reviews recent theoretical developments in heavy-quarkonium physics from the point of view of effective-field theories of QCD. We discuss nonrelativistic QCD and concentrate on potential nonrelativistic QCD. The main goal will be to derive Schroedinger equations based on QCD that govern heavy-quarkonium physics in the weak- and strong-coupling regimes. Finally, the review discusses a selected set of applications, which include spectroscopy, inclusive decays, and electromagnetic threshold production

Consistent Kaluza-Klein truncations via exceptional field theory

Energy Technology Data Exchange (ETDEWEB)

Hohm, Olaf [Center for Theoretical Physics, Massachusetts Institute of Technology,Cambridge, MA 02139 (United States); Samtleben, Henning [Université de Lyon, Laboratoire de Physique, UMR 5672, CNRS,École Normale Supérieure de Lyon, 46, allée d’Italie, F-69364 Lyon cedex 07 (France)

2015-01-26

We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO(p,q) and CSO(p,q,r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides H{sup p,q}, thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D=11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS{sub 5}×S{sup 5}), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.

Uncertainty quantification theory, implementation, and applications

CERN Document Server

Smith, Ralph C

2014-01-01

The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers ca...

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

International Conference Modern Stochastics: Theory and Applications III

CERN Document Server

Limnios, Nikolaos; Mishura, Yuliya; Sakhno, Lyudmyla; Shevchenko, Georgiy; Modern Stochastics and Applications

2014-01-01

This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a  great source of inspiration for designing new algorithms, modeling procedures, and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas, and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision making, mathematical finance, mathematical physics, and economics. Contributions to this Work include those of selected speakers from the international conference entitled “Modern Stochastics: Theory and Applications III,”  held on September 10 –14, 2012 at Taras Shevchenko National University of Kyiv, Ukraine. The conference covered the following areas of research in probability theory and its applications: stochastic analysis, stochastic processes and fields, random matrices, optimization methods in probability, st...

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)

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.)

On quantum field theory in gravitational background

International Nuclear Information System (INIS)

Haag, R.; Narnhofer, H.; Stein, U.

1984-02-01

We discuss Quantum Fields on Riemannian space-time. A principle of local definitness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows to formulate local stability. In application to a region with a time-like Killing vector field and horizons it yields the value of the Hawking temperature. The concept of vacuum and particles in a non stationary metric is treated in the example of the Robertson-Walker metric and some remarks on detectors in non inertial motion are added. (orig.)

Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian gauge theories, and gravitation. 4. ed.; Theoretische Physik 3. Klassische Feldtheorie. Von Elektrodynamik, nicht-Abelschen Eichtheorien und Gravitation

Energy Technology Data Exchange (ETDEWEB)

Scheck, Florian [Mainz Univ. (Germany). Inst. fuer Physik

2017-09-01

The following topics are dealt with: Maxwell's equations together with their symmetry and covariance, the Maxwell theory as classical field theory, simple applications of Maxwell's theory, local gauge theories, classical field theory of gravitation. (HSI)

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.

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

Noncommutative analysis, operator theory and applications

CERN Document Server

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

2016-01-01

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

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.)

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.

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.

Motion of small bodies in classical field theory

International Nuclear Information System (INIS)

Gralla, Samuel E.

2010-01-01

I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

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.

Quantum κ-deformed differential geometry and field theory

Science.gov (United States)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

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

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.)

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...

Comparing Theory and Practice: An Application of Complexity Theory to General Ridgway’s Success in Korea

Science.gov (United States)

2010-12-02

will face in an uncertain future. Complexity Theory , History, Practice, Military Theory , Leadership 14. SUBJECT TERMS 70 15. NUMBER OF PAGES...complexity theory : scale, adaptive leadership , and bottom up feedback from the agents (the soldiers in the field). These are all key sub components of...Approved for Public Release; Distribution is Unlimited COMPARING THEORY AND PRACTICE: AN APPLICATION OF COMPLEXITY THEORY TO GENERAL RIDGWAY’S

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...

Non-integrable quantum field theories as perturbations of certain integrable models

International Nuclear Information System (INIS)

Delfino, G.; Simonetti, P.

1996-03-01

We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ T c and the scaling region around the minimal model M 2 , τ . For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian. (author). 41 refs, 9 figs, 1 tab

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

Light-front field theory in the description of hadrons

Directory of Open Access Journals (Sweden)

Ji Chueng-Ryong

2017-01-01

Full Text Available We discuss the use of light-front field theory in the descriptions of hadrons. In particular, we clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame and the light-front dynamics and the advantage of the light-front dynamics in hadron physics. As an application, we present our recent work on the flavor asymmetry in the proton sea and identify the presence of the delta-function contributions associated with end-point singularities arising from the chiral effective theory calculation. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.

Light-front field theory in the description of hadrons

Science.gov (United States)

Ji, Chueng-Ryong

2017-03-01

We discuss the use of light-front field theory in the descriptions of hadrons. In particular, we clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame and the light-front dynamics and the advantage of the light-front dynamics in hadron physics. As an application, we present our recent work on the flavor asymmetry in the proton sea and identify the presence of the delta-function contributions associated with end-point singularities arising from the chiral effective theory calculation. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.

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

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.

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.)

Game Theory - Its Applications to Ethical Decision Making

Directory of Open Access Journals (Sweden)

Cavagnetto Stefano

2014-01-01

Full Text Available The application of game theory according to Hargreaves-Heap and Varonfakis (1995 to understand human behaviour, and in particular ethical behaviour, is a valuable development, as game theory has gradually become one of the key frameworks to assist us in the understanding of social sciences. Esther (1982 and Aumann and Hart (1992 show that there are several studies that indicate the importance of a game theoretic framework in advancing our understanding of social behaviour and evolutionary sciences. Although the application of game theory in the above areas has largely been not formalised, its application in the fields of ethical conduct and human behaviour is at present developed in several respects with the gradual assistance of advances in related areas such as evolutionary biology and our understanding of group social behaviour.

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)

Quantum mean-field theory of collective dynamics and tunneling

International Nuclear Information System (INIS)

Negele, J.W.

1981-01-01

A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures

Relativistic many-body theory a new field-theoretical approach

CERN Document Server

Lindgren, Ingvar

2016-01-01

This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title.  In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...

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)

Electron traps in polar liquids. An application of the formalism of the random field theory

International Nuclear Information System (INIS)

Hilczer, M.; Bartczak, W.M.

1992-01-01

The potential energy surface in a disordered medium is described, using the concepts of the mathematical theory of random fields. The statistics of trapping sites (the regions of an excursion of the random field) is obtained for liquid methanol as a numerical example of the theory. (author). 15 refs, 4 figs

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

International Nuclear Information System (INIS)

Hilczer, M.; Bartczak, W.M.

1993-01-01

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

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

Group theory for chemists fundamental theory and applications

CERN Document Server

Molloy, K C

2010-01-01

The basics of group theory and its applications to themes such as the analysis of vibrational spectra and molecular orbital theory are essential knowledge for the undergraduate student of inorganic chemistry. The second edition of Group Theory for Chemists uses diagrams and problem-solving to help students test and improve their understanding, including a new section on the application of group theory to electronic spectroscopy.Part one covers the essentials of symmetry and group theory, including symmetry, point groups and representations. Part two deals with the application of group theory t

Algebric generalization of symmetry Dirac bracket. Application to field theory

International Nuclear Information System (INIS)

Rocha Filho, T.M. da.

1987-01-01

The A set of observable of a physical system with finite e infinite number of degrees of freedom and submitted to certain constraint conditions, is considered. Using jordan algebra structure on A in relation to bymmetric Poisson bracket obtained by Droz-Vincent, a jordan product is obtained on the A/I quocient set with regard to I ideal generated by constraints of second class. It is shown that this product on A/I corresponds to symmetric Dirac bracket. The developed formulation is applied to a system corresponding to harmonic oscillators, non relativistic field, Rarita-Schwinger field and the possibility of its utilization in fermionic string theories is discussed. (M.C.K.)

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

Light cone sum rules in nonabelian gauge field theory

Energy Technology Data Exchange (ETDEWEB)

Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

1981-03-24

The author examines, in the context of nonabelian gauge field theory, the derivation of the light cone sum rules which were obtained earlier on the assumption of dominance of canonical singularity in the current commutator on the light cone. The retarded scaling functions appearing in the sum rules are numbers known in terms of the charges of the quarks and the number of quarks and gluons in the theory. Possible applications of the sum rules are suggested.

A general solution of the BV-master equation and BRST field theories

International Nuclear Information System (INIS)

Dayi, O.F.

1993-05-01

For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization. (author). 17 refs

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.

Quantum theory of gauge fields and rigid processes calculation

International Nuclear Information System (INIS)

Andreev, I.V.

1981-01-01

Elementary statement of the basic data on the nature of quark interactions and their role in the high energy processes is presented in the first part of the paper. The second part of the paper deals with gauge theory (GT) of strong interactions (chromodynamics (CD)) and its application in calculation of rigid processes with quark participation. It is based on the method of functional integration (MFI). A comparatively simple representation of the MFI in the quantum theory and formulation of the perturbation theory for gauge fields are given. A derivation of the rules of diagram technique is presented. Renormalization invariance of the theory and the basic for CD phenomenon of asymptotical freedom are discussed. Theory application in calculation of certain effects at high energies is considered. From the CD view point considered is a parton model on the base of which ''rigid'' stage of evolution of quark and gluon jets produced at high energies can be quantitatively described and some quantitative experimental tests of the CD are suggested [ru

Quantum scattering from classical field theory

International Nuclear Information System (INIS)

Gould, T.M.; Poppitz, E.R.

1995-01-01

We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial-value conditions. The initial-value conditions are such as to make the solution of the classical field equations amenable to numerical methods. We propose a practical procedure for computing classical solutions which contribute to high energy two-particle scattering amplitudes. We consider in this regard the implications of a recent numerical simulation in classical SU(2) Yang-Mills theory for multiparticle scattering in quantum gauge theories and speculate on its generalization to electroweak theory. We also generalize our results to the case of complex trajectories and discuss the prospects for finding a solution to the resulting complex boundary value problem, which would allow the application of our method to any wave packet to coherent state transition. Finally, we discuss the relevance of these results to the issues of baryon number violation and multiparticle scattering at high energies. ((orig.))

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)

Conformal Field Theory, Automorphic Forms and Related Topics

CERN Document Server

Weissauer, Rainer; CFT 2011

2014-01-01

This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.   The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster, and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson.   The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the MAThematics Center Heidelberg (MATCH).

Compositional Data Analysis Theory and Applications

CERN Document Server

Pawlowsky-Glahn, Vera

2011-01-01

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

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.)

Integrable models in 1+1 dimensional quantum field theory

International Nuclear Information System (INIS)

Faddeev, Ludvig.

1982-09-01

The goal of this lecture is to present a unifying view on the exactly soluble models. There exist several reasons arguing in favor of the 1+1 dimensional models: every exact solution of a field-theoretical model can teach about the ability of quantum field theory to describe spectrum and scattering; some 1+1 d models have physical applications in the solid state theory. There are several ways to become acquainted with the methods of exactly soluble models: via classical statistical mechanics, via Bethe Ansatz, via inverse scattering method. Fundamental Poisson bracket relation FPR and/or fundamental commutation relations FCR play fundamental role. General classification of FPR is given with promizing generalizations to FCR

Noncommutative Geometry in M-Theory and Conformal Field Theory

International Nuclear Information System (INIS)

Morariu, Bogdan

1999-01-01

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U q (SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models

Noncommutative Geometry in M-Theory and Conformal Field Theory

Energy Technology Data Exchange (ETDEWEB)

Morariu, Bogdan [Univ. of California, Berkeley, CA (United States)

1999-05-01

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

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

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.

Superconformal partial waves in Grassmannian field theories

Energy Technology Data Exchange (ETDEWEB)

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

2015-12-23

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

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.)

New numerical methods for quantum field theories on the continuum

Energy Technology Data Exchange (ETDEWEB)

Emirdag, P.; Easter, R.; Guralnik, G.S.; Hahn, S.C

2000-03-01

The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the accuracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear {sigma} model is outlined.

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.

Complex Time-Delay Systems Theory and Applications

CERN Document Server

Atay, Fatihcan M

2010-01-01

Time delays in dynamical systems arise as an inevitable consequence of finite speeds of information transmission. Realistic models increasingly demand the inclusion of delays in order to properly understand, analyze, design, and control real-life systems. The goal of this book is to present the state-of-the-art in research on time-delay dynamics in the framework of complex systems and networks. While the mathematical theory of delay equations is quite mature, its application to the particular problems of complex systems and complexity is a newly emerging field, and the present volume aims to play a pioneering role in this perspective. The chapters in this volume are authored by renowned experts and cover both theory and applications in a wide range of fields, with examples extending from neuroscience and biology to laser physics and vehicle traffic. Furthermore, all chapters include sufficient introductory material and extensive bibliographies, making the book a self-contained reference for both students and ...

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.)

Entanglement entropy in scalar field theory on the fuzzy sphere

International Nuclear Information System (INIS)

Okuno, Shizuka; Suzuki, Mariko; Tsuchiya, Asato

2016-01-01

We study entanglement entropy on the fuzzy sphere. We calculate it in a scalar field theory on the fuzzy sphere, which is given by a matrix model. We use a method that is based on the replica method and applicable to interacting fields as well as free fields. For free fields, we obtain results consistent with the previous study, which serves as a test of the validity of the method. For interacting fields, we perform Monte Carlo simulations at strong coupling and see a novel behavior of entanglement entropy

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

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

Implementation of static generalized perturbation theory for LWR design applications

International Nuclear Information System (INIS)

Byron, R.F.; White, J.R.

1987-01-01

A generalized perturbation theory (GPT) formulation is developed for application to light water reactor (LWR) design. The extensions made to standard generalized perturbation theory are the treatment of thermal-hydraulic and fission product poisoning feedbacks, and criticality reset. This formulation has been implemented into a standard LWR design code. The method is verified by comparing direct calculations with GPT calculations. Data are presented showing that feedback effects need to be considered when using GPT for LWR problems. Some specific potential applications of this theory to the field of LWR design are discussed

Applications of the renormalization group approach to problems in quantum field theory

International Nuclear Information System (INIS)

Renken, R.L.

1985-01-01

The presence of fluctuations at many scales of length complicates theories of quantum fields. However, interest is often focused on the low-energy consequences of a theory rather than the short distance fluctuations. In the renormalization-group approach, one takes advantage of this by constructing an effective theory with identical low-energy behavior, but without short distance fluctuations. Three problems of this type are studied here. In chapter 1, an effective lagrangian is used to compute the low-energy consequences of theories of technicolor. Corrections to weak-interaction parameters are found to be small, but conceivably measurable. In chapter 2, the renormalization group approach is applied to second order phase transitions in lattice gauge theories such as the deconfining transition in the U(1) theory. A practical procedure for studying the critical behavior based on Monte Carlo renormalization group methods is described in detail; no numerical results are presented. Chapter 3 addresses the problem of computing the low-energy behavior of atoms directly from Schrodinger's equation. A straightforward approach is described, but is found to be impractical

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

Directory of Open Access Journals (Sweden)

František FOJTÍK

2014-06-01

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

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

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

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.

Spectral theory and nonlinear analysis with applications to spatial ecology

CERN Document Server

Cano-Casanova, S; Mora-Corral , C

2005-01-01

This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.

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.

Relativistic Many-Body Theory A New Field-Theoretical Approach

CERN Document Server

Lindgren, Ingvar

2011-01-01

Relativistic Many-Body Theory treats — for the first time — the combination of relativistic atomic many-body theory with quantum-electrodynamics (QED) in a unified manner. This book can be regarded as a continuation of the book by Lindgren and Morrison, Atomic Many-Body Theory (Springer 1986), which deals with the non-relativistic theory of many-electron systems, describing several means of treating the electron correlation to essentially all orders of perturbation theory. The treatment of the present book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insuffici...

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...

Grassmann phase space methods for fermions. II. Field theory

Energy Technology Data Exchange (ETDEWEB)

Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)

2017-02-15

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

Grassmann phase space methods for fermions. II. Field theory

International Nuclear Information System (INIS)

Dalton, B.J.; Jeffers, J.; Barnett, S.M.

2017-01-01

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

Yang-Baxter algebra - Integrable systems - Conformal quantum field theories

International Nuclear Information System (INIS)

Karowski, M.

1989-01-01

This series of lectures is based on investigations [1,2] of finite-size corrections for the six-vertex model by means of Bethe ansatz methods. In addition a review on applications of Yang-Baxter algebras and an introduction to the theory of integrable systems and the algebraic Bethe ansatz is presented. A Θ-vacuum like angle appearing in the RSOS-models is discussed. The continuum limit in the critical case of these statistical models is performed to obtain the minimal models of conformal quantum field theory. (author)

Distributed hash table theory, platforms and applications

CERN Document Server

Zhang, Hao; Xie, Haiyong; Yu, Nenghai

2013-01-01

This SpringerBrief summarizes the development of Distributed Hash Table in both academic and industrial fields. It covers the main theory, platforms and applications of this key part in distributed systems and applications, especially in large-scale distributed environments. The authors teach the principles of several popular DHT platforms that can solve practical problems such as load balance, multiple replicas, consistency and latency. They also propose DHT-based applications including multicast, anycast, distributed file systems, search, storage, content delivery network, file sharing and c

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

Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications

International Nuclear Information System (INIS)

Cardy, John

2013-01-01

We describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal field theories with varying central charge c. Logarithmic behaviour arises from degeneracies in the spectrum of scaling dimensions at certain values of c. The theories we consider are all invariant under some internal symmetry group, and logarithmic behaviour occurs when the decomposition of the physical observables into irreducible operators becomes singular. Examples considered are quenched random magnets using the replica formalism, self-avoiding walks as the n → 0 limit of the O(n) model, and percolation as the limit Q → 1 of the Potts model. In these cases we identify logarithmic operators and pay particular attention to how the c → 0 paradox is resolved and how the b-parameter is evaluated. We also show how this approach gives information on logarithmic behaviour in the extended Ising model, uniform spanning trees and the O( − 2) model. Most of our results apply to general dimensionality. We also consider massive logarithmic theories and, in two dimensions, derive sum rules for the effective central charge and the b-parameter. (review)

A survey on the modeling and applications of cellular automata theory

Science.gov (United States)

Gong, Yimin

2017-09-01

The Cellular Automata Theory is a discrete model which is now widely used in scientific researches and simulations. The model is comprised of some cells which changes according to a specific rule over time. This paper provides a survey of the Modeling and Applications of Cellular Automata Theory, which focus on the program realization of Cellular Automata Theory and the application of Cellular Automata in each field, such as road traffic, land use, and cutting machines. Each application is further explained, and several related main models are briefly introduced. This research aims to help decision-makers formulate appropriate development plans.

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.

Logarithmic conformal field theory: beyond an introduction

International Nuclear Information System (INIS)

Creutzig, Thomas; Ridout, David

2013-01-01

studied here by first determining its irreducible spectrum, which turns out to be continuous, as well as a selection of natural reducible, but indecomposable, modules. This is followed by a detailed description of how to obtain character formulae for each irreducible, a derivation of the action of the modular group on the characters, and an application of the Verlinde formula to compute the Grothendieck fusion rules. In each case, the (genuine) fusion rules are known, so comparisons can be made and favourable conclusions drawn. In addition, each example admits an infinite set of simple currents, hence extended symmetry algebras may be constructed and a series of bulk modular invariants computed. The spectrum of such an extended theory is typically discrete and this is how the triplet model W(1,2) arises, for example. Moreover, simple current technology admits a derivation of the extended algebra fusion rules from those of its continuous parent theory. Finally, each example is concluded by a brief description of the computation of some bulk correlators, a discussion of the structure of the bulk state space, and remarks concerning more advanced developments and generalizations. The final part gives a very short account of the theory of staggered modules, the (simplest class of) representations that are responsible for the logarithmic singularities that distinguish logarithmic theories from their rational cousins. These modules are discussed in a generality suitable to encompass all the examples met in this review and some of the very basic structure theory is proven. Then, the important quantities known as logarithmic couplings are reviewed for Virasoro staggered modules and their role as fundamentally important parameters, akin to the three-point constants of rational conformal field theory, is discussed. An appendix is also provided in order to introduce some of the necessary, but perhaps unfamiliar, language of homological algebra. (review)

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

Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects

International Nuclear Information System (INIS)

Vary, J. P.

2012-01-01

Fundamental theories, such as quantum electrodynamics and quantum chromodynamics promise great predictive power addressing phenomena over vast scales from the microscopic to cosmic scales. However, new non-perturbative tools are required for physics to span from one scale to the next. I outline recent theoretical and computational progress to build these bridges and provide illustrative results for Hamiltonian Light Front Field Theory. One key area is our development of basis function approaches that cast the theory as a Hamiltonian matrix problem while preserving a maximal set of symmetries. Regulating the theory with an external field that can be removed to obtain the continuum limit offers additional possibilities as seen in an application to the anomalous magnetic moment of the electron. Recent progress capitalizes on algorithm and computer developments for setting up and solving very large sparse matrix eigenvalue problems. Matrices with dimensions of 20 billion basis states are now solved on leadership-class computers for their low-lying eigenstates and eigenfunctions. (author)

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...

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)

Nonstandard approximation schemes for lower dimensional quantum field theories

International Nuclear Information System (INIS)

Fitzpatrick, D.A.

1981-01-01

The purpose of this thesis has been to apply two different nonstandard approximation schemes to a variety of lower-dimensional schemes. In doing this, we show their applicability where (e.g., Feynman or Rayleigh-Schroedinger) approximation schemes are inapplicable. We have applied the well-known mean-field approximation scheme by Guralnik et al. to general lower dimensional theories - the phi 4 field theory in one dimension, and the massive and massless Thirring models in two dimensions. In each case, we derive a bound-state propagator and then expand the theory in terms of the original and bound-state propagators. The results obtained can be compared with previously known results thereby show, in general, reasonably good convergence. In the second half of the thesis, we develop a self-consistent quantum mechanical approximation scheme. This can be applied to any monotonic polynomial potential. It has been applied in detail to the anharmonic oscillator, and the results in several analytical domains are very good, including extensive tables of numerical results

Grassmann methods in lattice field theory and statistical mechanics

International Nuclear Information System (INIS)

Bilgici, E.; Gattringer, C.; Huber, P.

2006-01-01

Full text: In two dimensions models of loops can be represented as simple Grassmann integrals. In our work we explore the generalization of these techniques to lattice field theories and statistical mechanic systems in three and four dimensions. We discuss possible strategies and applications for representations of loop and surface models as Grassmann integrals. (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…

Text Mining Applications and Theory

CERN Document Server

Berry, Michael W

2010-01-01

Text Mining: Applications and Theory presents the state-of-the-art algorithms for text mining from both the academic and industrial perspectives.  The contributors span several countries and scientific domains: universities, industrial corporations, and government laboratories, and demonstrate the use of techniques from machine learning, knowledge discovery, natural language processing and information retrieval to design computational models for automated text analysis and mining. This volume demonstrates how advancements in the fields of applied mathematics, computer science, machine learning

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

Weyl consistency conditions in non-relativistic quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Pal, Sridip; Grinstein, Benjamín [Department of Physics, University of California,San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States)

2016-12-05

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2+1 dimensions with anisotropic scaling exponent z=2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. We comment on possible candidates for a C-theorem in higher dimensions.

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

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

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

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

Electricity markets theories and applications

CERN Document Server

Lin, Jeremy

2017-01-01

Electricity Markets: Theories and Applications offers students and practitioners a clear understanding of the fundamental concepts of the economic theories, particularly microeconomic theories, as well as information on some advanced optimization methods of electricity markets. The authors--noted experts in the field--cover the basic drivers for the transformation of the electricity industry in both the United States and around the world and discuss the fundamentals of power system operation, electricity market design and structures, and electricity market operations. The text also explores advanced topics of power system operations and electricity market design and structure including zonal versus nodal pricing, market performance and market power issues, transmission pricing, and the emerging problems electricity markets face in smart grid and micro-grid environments. The authors also examine system planning under the context of electricity market regime. They explain the new ways to solve problems with t...

Spectral theorem in noncommutative field theories: Jacobi dynamics

International Nuclear Information System (INIS)

Géré, Antoine; Wallet, Jean-Christophe

2015-01-01

Jacobi operators appear as kinetic operators of several classes of noncommutative field theories (NCFT) considered recently. This paper deals with the case of bounded Jacobi operators. A set of tools mainly issued from operator and spectral theory is given in a way applicable to the study of NCFT. As an illustration, this is applied to a gauge-fixed version of the induced gauge theory on the Moyal plane expanded around a symmetric vacuum. The characterization of the spectrum of the kinetic operator is given, showing a behavior somewhat similar to a massless theory. An attempt to characterize the noncommutative geometry related to the gauge fixed action is presented. Using a Dirac operator obtained from the kinetic operator, it is shown that one can construct an even, regular, weakly real spectral triple. This spectral triple does not define a noncommutative metric space for the Connes spectral distance. (paper)

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

Instantons and large N an introduction to non-perturbative methods in quantum field theory

CERN Document Server

Marino, Marcos

2015-01-01

This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang-Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behaviour of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.

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

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

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

Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

International Nuclear Information System (INIS)

Schenkel, Alexander

2011-01-01

quantum field theory at short distances, i.e. in the ultraviolet. In the third part we develop elements of a more powerful, albeit more abstract, mathematical approach to noncommutative gravity. The goal is to better understand global aspects of homomorphisms between and connections on noncommutative vector bundles, which are fundamental objects in the mathematical description of noncommutative gravity. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of modules is clarified, and as a consequence we are able to add tensor fields of arbitrary type to the noncommutative gravity theory of Wess et al. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.

Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Schenkel, Alexander

2011-10-24

noncommutative quantum field theory at short distances, i.e. in the ultraviolet. In the third part we develop elements of a more powerful, albeit more abstract, mathematical approach to noncommutative gravity. The goal is to better understand global aspects of homomorphisms between and connections on noncommutative vector bundles, which are fundamental objects in the mathematical description of noncommutative gravity. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of modules is clarified, and as a consequence we are able to add tensor fields of arbitrary type to the noncommutative gravity theory of Wess et al. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.

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)

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.

Cosmology in Gauge Field Theory and String Theory

International Nuclear Information System (INIS)

Garcia Compean, H

2005-01-01

This new book is intended for students and researchers who want to go into the interplay between cosmology and high-energy physics. It assumes a prior knowledge of these subjects such as some of the topics contained in the previous books by the authors, Introduction to Gauge Field Theory (1993 Bristol: Institute of Physics Publishing) and Supersymmetric Gauge Field Theory and String Theory (1994 Bristol: Institute of Physics Publishing). However, the book is intended to be self-contained, explaining, from a modern perspective, some background material mainly in standard cosmology, topological defects, baryogenesis, inflationary cosmology and, at the end of the book, some of the basics of string theory. What is distinctively new about this book is that it lies in the interplay between cosmology and high-energy physics typically above 100 GeV (10 15 K). Often these subjects are presented in regular textbooks in a disconnected way, or in research papers, proceedings and review papers but usually not in a pedagogical style. Thus, in this sense, the book is unique and deserves a special place in the recent literature. The book starts by reviewing the standard material of the early universe. The standard model of cosmology from a modern perspective is revised in chapter 1. In chapter 2, phase transitions in different models are discussed, Higgs, electroweak, GUTs, supersymmetric GUTs and supergravity, by using quantum field theory at finite temperature. Chapter 3 is devoted to a general account of topological defects and discusses how they arise as possible remnants of these phase transitions in GUTs. Other relics, such as neutrinos and axions, are introduced in chapter 5 and their impact in cosmology is assessed. In chapter 4, some of the most relevant mechanisms of baryogenesis are discussed in the context of the different GUTs and the minimal supersymmetric standard model (MSSM). Inflation is also discussed in the context of GUTs. In chapter 6, the authors introduce

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

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

On integration over Fermi fields in chiral and supersymmetric theories

International Nuclear Information System (INIS)

Vainshtein, A.I.; Zakharov, V.I.

1982-01-01

Chiral and supersymmetric theories are considered which cannot be formulated directly in Euclidean space or regularized by means of massive fields in a manifestly gauge invariant fashion. In case of so called real representations a simple recipe is proposed which allows for unambiguous evaluation of the fermionic determinant circumventing the difficulties mentioned. As application of the general technique the effective fermionic interactions induced by instantons of small size within simplest chiral and supesymmetric theories are calculated (SU(2) as the gauge group and one doublet of Weyl spinors or a triplet of Majorana spinors, respectively). In the latter case the effective Lagrangian violates explicitly invariance under supersymmetric transformations on the fermionic and vector fields defined in standard way [ru

Theories and control models and motor learning: clinical applications in neuro-rehabilitation.

Science.gov (United States)

Cano-de-la-Cuerda, R; Molero-Sánchez, A; Carratalá-Tejada, M; Alguacil-Diego, I M; Molina-Rueda, F; Miangolarra-Page, J C; Torricelli, D

2015-01-01

In recent decades there has been a special interest in theories that could explain the regulation of motor control, and their applications. These theories are often based on models of brain function, philosophically reflecting different criteria on how movement is controlled by the brain, each being emphasised in different neural components of the movement. The concept of motor learning, regarded as the set of internal processes associated with practice and experience that produce relatively permanent changes in the ability to produce motor activities through a specific skill, is also relevant in the context of neuroscience. Thus, both motor control and learning are seen as key fields of study for health professionals in the field of neuro-rehabilitation. The major theories of motor control are described, which include, motor programming theory, systems theory, the theory of dynamic action, and the theory of parallel distributed processing, as well as the factors that influence motor learning and its applications in neuro-rehabilitation. At present there is no consensus on which theory or model defines the regulations to explain motor control. Theories of motor learning should be the basis for motor rehabilitation. The new research should apply the knowledge generated in the fields of control and motor learning in neuro-rehabilitation. Copyright © 2011 Sociedad Española de Neurología. Published by Elsevier Espana. All rights reserved.

Application of γ field theory based calculation method to the monitoring of mine nuclear radiation environment

International Nuclear Information System (INIS)

Du Yanjun; Liu Qingcheng; Liu Hongzhang; Qin Guoxiu

2009-01-01

In order to find the feasibility of calculating mine radiation dose based on γ field theory, this paper calculates the γ radiation dose of a mine by means of γ field theory based calculation method. The results show that the calculated radiation dose is of small error and can be used to monitor mine environment of nuclear radiation. (authors)

Recent progress on the unified theory of polarization and coherence for stochastic electromagnetic fields

DEFF Research Database (Denmark)

Wang, Wei; Zhao, Juan; Hu, Xiaoying

2017-01-01

All optical fields undergo random fluctuation and the underlying theory referred to as coherence and polarization of optical fields has played a fundamental role as an important manifestation of the random fluctuations of the electric fields. In this paper, we reviewed our recent theoretical...... and experimental work on the unified theory of polarization and coherence including coherence tensor wave, degree of coherence tensor, degree of generalized Stokes parameters, and their applications including coherence tensor holography and two-point resolution of polarimetric imaging....

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

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

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

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...

Bayesian theory and applications

CERN Document Server

Dellaportas, Petros; Polson, Nicholas G; Stephens, David A

2013-01-01

The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and devel...

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 ...

Fuzzy pharmacology: theory and applications.

Science.gov (United States)

Sproule, Beth A; Naranjo, Claudio A; Türksen, I Burhan

2002-09-01

Fuzzy pharmacology is a term coined to represent the application of fuzzy logic and fuzzy set theory to pharmacological problems. Fuzzy logic is the science of reasoning, thinking and inference that recognizes and uses the real world phenomenon that everything is a matter of degree. It is an extension of binary logic that is able to deal with complex systems because it does not require crisp definitions and distinctions for the system components. In pharmacology, fuzzy modeling has been used for the mechanical control of drug delivery in surgical settings, and work has begun evaluating its use in other pharmacokinetic and pharmacodynamic applications. Fuzzy pharmacology is an emerging field that, based on these initial explorations, warrants further investigation.

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)

Integrable systems and quantum field theory. Works in progress Nr 75

International Nuclear Information System (INIS)

Baird, Paul; Helein, Frederic; Kouneiher, Joseph; Roubtsov, Volodya; Antunes, Paulo; Banos, Bertrand; Barbachoux, Cecile; Desideri, Laura; Kahouadji, Nabil; Gerding, Aaron; Heller, Sebastian; Schmitt, Nicholas; Harrivel, Dikanaina; Hoevenaars, Luuk K.; Iftime, Mihaela; Levy, Thierry; Lisovyy, Oleg; Masson, Thierry; Skrypnyk, Taras; Pedit, Franz; Egeileh, Michel

2009-01-01

The contributions of this collective book address the quantum field theory (integrable systems and quantum field theory, introduction to supermanifolds and supersymmetry, beyond geometric quantification, Gaussian measurements and Fock spaces), differential geometry and physics (gravitation and geometry, physical events and the superspace about the hole argument, the Cartan-Kaehler theory and applications to local isometric and conformal embedding, calibrations, Cabal-Yau structures and Monge-Ampere structures, Hamiltonian multi-symplectic formalism and Monge-Ampere equations, big bracket, derivations and derivative multi-brackets), integrable system, geometry and physics (finite-volume correlation functions of monodromy fields on the lattice with the Toeplitz representation, Frobenius manifolds and algebraic integrability, an introduction to twistors, Hamiltonian systems on the 'coupled' curves, Nambu-Poisson mechanics and Fairlie-type integrable systems, minimal surfaces with polygonal boundary and Fuchsian equations, global aspects of integrable surface geometry), and non commutative geometry (an informal introduction to the ideas and concepts of non commutative geometry)

Mean-field theory of spin-glasses with finite coordination number

Science.gov (United States)

Kanter, I.; Sompolinsky, H.

1987-01-01

The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.

Stochastic Gravity: Theory and Applications

Directory of Open Access Journals (Sweden)

Hu Bei Lok

2004-01-01

Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction

Application of Canonical Effective Methods to Background-Independent Theories

Science.gov (United States)

Buyukcam, Umut

Effective formalisms play an important role in analyzing phenomena above some given length scale when complete theories are not accessible. In diverse exotic but physically important cases, the usual path-integral techniques used in a standard Quantum Field Theory approach seldom serve as adequate tools. This thesis exposes a new effective method for quantum systems, called the Canonical Effective Method, which owns particularly wide applicability in backgroundindependent theories as in the case of gravitational phenomena. The central purpose of this work is to employ these techniques to obtain semi-classical dynamics from canonical quantum gravity theories. Application to non-associative quantum mechanics is developed and testable results are obtained. Types of non-associative algebras relevant for magnetic-monopole systems are discussed. Possible modifications of hypersurface deformation algebra and the emergence of effective space-times are presented. iii.

Ab initio Hamiltonian approach to light nuclei and quantum field theory