scholarly journals Quantization and Perturbation Theory of the Non-Abelian Gauge Theory Confined in the One-Dimensional Bag

1976 ◽  
Vol 56 (1) ◽  
pp. 284-296
Author(s):  
T. Yoneya
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
One Dimensional ◽  
The One

scholarly journals TRANSVERSE WARD–TAKAHASHI RELATION FOR THE FERMION–BOSON VERTEX TO ONE-LOOP ORDER

2006 ◽  
Vol 21 (12) ◽  
pp. 2541-2551 ◽  
Author(s):  
HAN-XIN HE ◽  
F. C. KHANNA
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Loop Order ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Transverse Part ◽  
Feynman Rules ◽  
Covariant Gauge ◽  
The One ◽  
Massless Fermions

In this paper, the transverse Ward–Takahashi relation for the fermion–boson vertex in momentum space is derived in four-dimensional Abelian gauge theory. We show that, by a formal derivation, the transverse Ward–Takahashi relation to one-loop order is satisfied. We also calculate the transverse Ward–Takahashi relation to one-loop order in an arbitrary covariant gauge in the case of massless fermions and find that the result is exactly the same as we obtain in terms of the one-loop fermion–boson vertex calculated in perturbation theory by using Feynman rules. This provides an approach to determine the transverse part of the vertex.

scholarly journals FEYNMAN PERTURBATION THEORY FOR GAUGE THEORY ON TRANSVERSE LATTICE

2010 ◽  
Vol 25 (18n19) ◽  
pp. 3621-3640
Author(s):  
M. S. KARNEVSKIY ◽  
S. A. PASTON
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Degrees Of Freedom ◽  
Rotational Invariance ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Transverse Lattice ◽  
Abelian Gauge Theory ◽  
Independent Variables ◽  
Ultraviolet Regularization

Feynman perturbation theory for non-Abelian gauge theory in light-like gauge is investigated. A lattice along two spacelike directions is used as a gauge invariant ultraviolet regularization. For preservation of the polynomiality of action, we use as independent variables arbitrary (nonunitary) matrices related to the link of the lattice. The action of the theory is selected in such a way to preserve as much as possible the rotational invariance, which remains after an introduction of the lattice, as well as to make superfluous degrees of freedom vanish in the limit of removing the regularization. Feynman perturbation theory is constructed and diagrams which does not contain ultraviolet divergences are analyzed. The scheme of renormalization of this theory is discussed.

scholarly journals ON THE HOLOMORPHICALLY FACTORIZED PARTITION FUNCTION FOR ABELIAN GAUGE THEORY IN SIX DIMENSIONS

2002 ◽  
Vol 17 (03) ◽  
pp. 383-393 ◽  
Author(s):  
ANDREAS GUSTAVSSON
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Gauge Field ◽  
Hamiltonian Formulation ◽  
Partition Functions ◽  
Modular Invariant ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Six Dimensions ◽  
The One

We use holomorphic factorization to find the partition functions of an Abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that previously has been found in a Hamiltonian formulation.

scholarly journals Parity-odd fragmentation functions

2019 ◽  
Vol 34 (25) ◽  
pp. 1950144 ◽  
Author(s):  
Weihua Yang
Keyword(s):  
Gauge Theory ◽  
Quantum Chromodynamics ◽  
Strong Interactions ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
One Dimensional ◽  
Parity Symmetry ◽  
Fragmentation Functions ◽  
Definition Of ◽  
Operator Definition

Quantum chromodynamics is a non-Abelian gauge theory of strong interactions, in which the parity symmetry can be violated by the nontrivial [Formula: see text]-vacuum tunneling effects. The [Formula: see text]-vacuum induces the local parity-odd domains. Those reactions that occur in these domains can be affected by the tunneling effects and quantities become parity-odd. In this paper we consider the fragmentation process where parity-odd fragmentation functions are introduced. We present the fragmentation functions by decomposing the quark–quark correlator. Among the total 16 fragmentation functions, eight of them are parity conserved, and the others are parity violated. They have a one-to-one correspondence. Positivity bounds of these one-dimensional fragmentation functions are shown. To be explicit, we also introduce an operator definition of the parity-odd correlator. According to the definition, we give a proof that the parity-odd fragmentation functions are local quantities and vanish when sum over all the hadrons [Formula: see text].

Regge behavior of spontaneously broken non-Abelian gauge theory

1978 ◽  
Vol 17 (2) ◽  
pp. 585-597 ◽  
Author(s):  
J. B. Bronzan ◽  
R. L. Sugar
Keyword(s):  
Gauge Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Regge Behavior

scholarly journals Static force potential of a non-Abelian gauge theory in a finite box in Coulomb gauge

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Tomohiro Furukawa ◽  
Keiichi Ishibashi ◽  
H. Itoyama ◽  
Satoshi Kambayashi
Keyword(s):  
Gauge Theory ◽  
Coulomb Gauge ◽  
Static Force ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Force Potential

Non-Abelian gauge theory from the Poisson bracket

2018 ◽  
Vol 33 (30) ◽  
pp. 1850182
Author(s):  
Mu Yi Chen ◽  
Su-Long Nyeo
Keyword(s):  
Gauge Theory ◽  
Poisson Bracket ◽  
Commutation Relation ◽  
Maxwell Equations ◽  
Dynamical Variable ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Generalized Poisson ◽  
Lie Algebraic Structure

The Hamiltonian of a nonrelativistic particle coupled to non-Abelian gauge fields is defined to construct a non-Abelian gauge theory. The Hamiltonian which includes isospin as a dynamical variable dictates the dynamics of the particle and isospin according to the Poisson bracket that incorporates the Lie algebraic structure of isospin. The generalized Poisson bracket allows us to derive Wong’s equations, which describe the dynamics of isospin, and the homogeneous (sourceless) equations for non-Abelian gauge fields by following Feynman’s proof of the homogeneous Maxwell equations.It is shown that the derivation of the homogeneous equations for non-Abelian gauge fields using the generalized Poisson bracket does not require that Wong’s equations be defined in the time-axial gauge, which was used with the commutation relation. The homogeneous equations derived by using the commutation relation are not Galilean and Lorentz invariant. However, by using the generalized Poisson bracket, it can be shown that the homogeneous equations are not only Galilean and Lorentz invariant but also gauge independent. In addition, the quantum ordering ambiguity that arises from using the commutation relation can be avoided when using the Poisson bracket.From the homogeneous equations, which define the “electric field” and “magnetic field” in terms of non-Abelian gauge fields, we construct the gauge and Lorentz invariant Lagrangian density and derive the inhomogeneous equations that describe the interaction of non-Abelian gauge fields with a particle.

scholarly journals Nilpotent symmetries and Curci–Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

2017 ◽  
Vol 32 (33) ◽  
pp. 1750193 ◽  
Author(s):  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
The Self ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Abelian Theory ◽  
Matter Fields

We derive the off-shell nilpotent symmetries of the two [Formula: see text]-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci–Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen [Formula: see text]-dimensional supermanifold. The latter is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] (with [Formula: see text]) are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] obey the relationships: [Formula: see text], [Formula: see text]. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

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