scholarly journals EXTENSION OF CHERN–SIMONS FORMS AND NEW GAUGE ANOMALIES

2014 ◽  
Vol 29 (03n04) ◽  
pp. 1450027 ◽  
Author(s):  
IGNATIOS ANTONIADIS ◽  
GEORGE SAVVIDY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field ◽  
Gauge Invariant ◽  
Higher Rank ◽  
Gauge Anomalies ◽  
Chern Simons

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher-rank field-strength tensors. The integrals of these forms over the corresponding space–time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern–Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions.

scholarly journals Some comments on infinities on quantum field theory: A functional integral approach

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Luiz C. L. Botelho
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Function Space ◽  
Functional Integral ◽  
Field Theories ◽  
Integral Approach ◽  
Quantum Field ◽  
Functional Integrals ◽  
Euclidean Field ◽  
The Subject

AbstractWe analyze on the formalism of probabilities measures-functional integrals on function space the problem of infinities on Euclidean field theories. We also clarify and generalize our previous published studies on the subject.

scholarly journals NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION

2008 ◽  
Vol 18 (09) ◽  
pp. 2787-2791
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Higgs Mechanism ◽  
Nonlinear Phenomena ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Statistical System ◽  
Equilibrium Limit ◽  
Euclidean Quantum Field Theory

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.

scholarly journals ON ALGEBRAIC STRUCTURES IMPLICIT IN TOPOLOGICAL QUANTUM FIELD THEORIES

1999 ◽  
Vol 08 (02) ◽  
pp. 125-163 ◽  
Author(s):  
Louis Crane ◽  
David Yetter
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Tensor Category ◽  
Topological Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Natural Way

We show that any 3D topological quantum field theory satisfying physically reasonable factorizability conditions has associated to it in a natural way a Hopf algebra object in a suitable tensor category. We also show that all objects in the tensor category have the structure of left-left crossed bimodules over the Hopf algebra object. For 4D factorizable topological quantum filed theories, we provide by analogous methods a construction of a Hopf algebra category.

Interacting Fields

2021 ◽  
pp. 237-252
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Field Theories ◽  
Green Functions ◽  
Quantum Field ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Feynman Rules ◽  
Wightman Axioms

We present a simple form of the Wightman axioms in a four-dimensional Minkowski space-time which are supposed to define a physically interesting interacting quantum field theory. Two important consequences follow from these axioms. The first is the invariance under CPT which implies, in particular, the equality of masses and lifetimes for particles and anti-particles. The second is the connection between spin and statistics. We give examples of interacting field theories and develop the perturbation expansion for Green functions. We derive the Feynman rules, both in configuration and in momentum space, for some simple interacting theories. The rules are unambiguous and allow, in principle, to compute any Green function at any order in perturbation.

Integrable Quantum Field Theories

2020 ◽  
pp. 575-621
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Theory ◽  
Integrable Quantum ◽  
Set Up ◽  
Integrable Quantum Field Theory

Chapter 16 covers the general properties of the integrable quantum field theories, including how an integrable quantum field theory is characterized by an infinite number of conserved charges. These theories are illustrated by means of significant examples, such as the Sine–Gordon model or the Toda field theories based on the simple roots of a Lie algebra. For the deformations of a conformal theory, it shown how to set up an efficient counting algorithm to prove the integrability of the corresponding model. The chapter focuses on two-dimensional models, and uses the term ‘two-dimensional’ to denote both a generic two-dimensional quantum field theory as well as its Euclidean version.

The Principles of Renormalisation

2021 ◽  
pp. 304-328
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Power Counting ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Green Functions ◽  
Quantum Field Theories ◽  
Quantum Field

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the classification of quantum field theories into non-renormalisable, renormalisable and super-renormalisable. We describe some regularisation schemes with particular emphasis on dimensional regularisation. The renormalisation programme is described at one loop order for φ‎4 and QED. We argue, without presenting the detailed proof, that the programme can be extended to any finite order in the perturbation expansion for every renormalisable (or super-renormalisable) quantum field theory. We derive the equation of the renormalisation group and explain how it can be used in order to study the asymptotic behaviour of Green functions. This makes it possible to introduce the concept of asymptotic freedom.

scholarly journals Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

2019 ◽  
Vol 34 (02) ◽  
pp. 1950010 ◽  
Author(s):  
A. N. Ivanov ◽  
R. Höllwieser ◽  
N. I. Troitskaya ◽  
M. Wellenzohn ◽  
Ya. A. Berdnikov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Electron Energy ◽  
Low Energy ◽  
Radiative Corrections ◽  
Quantum Field ◽  
Neutron Lifetime ◽  
Gauge Invariant ◽  
Hadronic Structure ◽  
Lepton Current

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.

scholarly journals TOWARDS A CLASSIFICATION OF FINITE FIELD THEORIES

1994 ◽  
Vol 09 (27) ◽  
pp. 2555-2567
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Field ◽  
Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Finiteness Conditions ◽  
Gauge Groups ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for gauge groups SU (n)(n>6) and a rather general particle content. It is shown that in the class of theories considered (149 different particle contents), only two models are able to fulfill the finiteness conditions. Only one of these is supersymmetric. For the nonsupersymmetric one the appropriate Yukawa couplings are constructed explicitly.

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