BRST QUANTIZATION OF GAUGE THEORIES ON THE HYPERSPHERE

1991 ◽  
Vol 06 (24) ◽  
pp. 2201-2203 ◽  
Author(s):  
D. G. C. McKEON
Keyword(s):  
Vector Field ◽  
Gauge Field ◽  
Gauge Theories ◽  
Brst Quantization ◽  
Radial Component ◽  
Effective Lagrangian ◽  
Abelian Case ◽  
Gauge Fixing

Drummond and Shore have shown that the most convenient gauge fixing term for gauge theories on a hypersphere is not a perfect square. We show how BRST quantization can be used to generate this gauge fixing term. This involves the introduction of two ghost fields, ci and [Formula: see text], the second of which is an anticommuting vector field. In the Abelian case, only the radial component of [Formula: see text] enters the effective Lagrangian; this is true in the non-Abelian case only if the gauge field is tangential to the hypersphere.

scholarly journals Remarks on gauge fixing and BRST quantization of noncommutative gauge theories

2005 ◽  
Vol 35 (3a) ◽  
pp. 645-651 ◽  
Author(s):  
Ricardo Amorim ◽  
Henrique Boschi-Filho ◽  
Nelson R. F. Braga
Keyword(s):  
Gauge Theories ◽  
Brst Quantization ◽  
Gauge Fixing ◽  
Noncommutative Gauge Theories

A study of the path-integral quantization of Abelian gauge theories when no explicit gauge-fixing term is included in the bilinear part of the gauge-field action

1985 ◽  
Vol 63 (10) ◽  
pp. 1334-1336
Author(s):  
Stephen Phillips
Keyword(s):  
Gauge Field ◽  
Path Integral ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Abelian Gauge ◽  
Gaussian Form ◽  
Path Integral Quantization ◽  
Field Action ◽  
Gauge Fixing

The mathematical problem of inverting the operator [Formula: see text] as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article.Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, [Formula: see text], can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one.Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action.

Abelian gauge theories: The framework of quantum electrodynamics (QED)

2021 ◽  
pp. 507-547
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Vector Field ◽  
Scalar Field ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
Four Dimensions ◽  
Gauge Fixing

This chapter is devoted Abelian gauge theory, whose physical realization is quantum electrodynamics (QED). Since many textbooks deal extensively with QED, the chapter focusses mainly on the more formal properties of Abelian gauge theories. First, the free massive vector field is considered, because its quantization does not immediately follow from the quantization of the scalar field, and thus requires a specific analysis. If the vector field is coupled to a conserved current, it is possible to construct a field theory with fermion matter renormalizable in four dimensions. In this case, a massless vector limit can be defined, and the corresponding field theory is gauge invariant. To directly quantize a gauge theory starting directly from first principles, it is necessary to introduce gauge fixing. The formal equivalence between different gauges is established. The Abelian gauge symmetry, broken by gauge-fixing terms, leads to a set of Ward–Takahashi (WT) identities which are used to prove the renormalizability of the quantum field theory (QFT). Renormalization group (RG) equations follow, and the RG β-function is calculated at leading order. As an introduction to the Standard Model of particle physics, the Abelian Landau–Ginzburg–Higgs model is described, where the gauge field is coupled to a complex scalar field with a non-zero expectation value, leading to a model that classically also describes a superconductor in a magnetic field.

scholarly journals HEAT KERNEL OF NONMINIMAL GAUGE FIELD KINETIC OPERATORS ON MOYAL PLANE

2007 ◽  
Vol 22 (01) ◽  
pp. 181-202 ◽  
Author(s):  
ALEXEI STRELCHENKO
Keyword(s):  
Heat Kernel ◽  
Gauge Field ◽  
Deformation Parameter ◽  
Gauge Theories ◽  
Gauge Model ◽  
Heat Trace ◽  
Gauge Fixing ◽  
Heat Expansion ◽  
Moyal Plane ◽  
The One

We generalize the Endo formula1 originally developed for the computation of the heat kernel asymptotic expansion for nonminimal operators in commutative gauge theories to the noncommutative case. In this way, the first three nonzero heat trace coefficients of the nonminimal U (N) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the nonplanar part of the heat trace asymptotics is determined by U (1) sector of the gauge model. The nonplanar or mixed heat kernel coefficients are shown to be gauge-fixing dependent in any dimension of space–time. In the case of the degenerate deformation parameter the lowest mixed coefficients in the heat expansion produce nonlocal gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U (N) model at one-loop level. Such phenomenon was observed at first in Ref. 2 for spacelike noncommutative ϕ4 scalar and U (1) gauge theories. The twisted-gauge transformation approach is discussed.

scholarly journals Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

scholarly journals SUPERFIELD FORMULATION OF THE LAGRANGIAN BRST QUANTIZATION METHOD

1995 ◽  
Vol 10 (35) ◽  
pp. 2687-2694 ◽  
Author(s):  
P.M. LAVROV ◽  
P.YU. MOSHIN ◽  
A.A. RESHETNYAK
Keyword(s):  
Gauge Theories ◽  
Brst Quantization ◽  
Brst Symmetry ◽  
Quantization Method ◽  
Ward Identities ◽  
S Matrix ◽  
General Gauge ◽  
Quantization Rules

Lagrangian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the S-matrix on a choice of the gauge is proved. The Ward identities in terms of superfields are derived.

scholarly journals Toy model for breaking super gauge theories at the effective Lagrangian level

1998 ◽  
Vol 57 (1) ◽  
pp. 170-179 ◽  
Author(s):  
Francesco Sannino ◽  
Joseph Schechter
Keyword(s):  
Gauge Theories ◽  
Effective Lagrangian

scholarly journals On gauge independence for gauge models with soft breaking of BRST symmetry

2014 ◽  
Vol 29 (30) ◽  
pp. 1450184 ◽  
Author(s):  
Alexander Reshetnyak
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Landau Gauge ◽  
Functional Integral ◽  
Yang Mills ◽  
Gauge Models ◽  
S Matrix ◽  
Gauge Fixing ◽  
Dependent Parameter ◽  
Quantum Treatment

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

scholarly journals ON THE QUANTUM CHROMODYNAMICS OF A MASSIVE VECTOR FIELD IN THE ADJOINT REPRESENTATION

2013 ◽  
Vol 28 (14) ◽  
pp. 1350054 ◽  
Author(s):  
ALFONSO R. ZERWEKH
Keyword(s):  
Vector Field ◽  
Quantum Chromodynamics ◽  
Extra Dimensions ◽  
Scalar Fields ◽  
Discrete Symmetry ◽  
Adjoint Representation ◽  
Coupling Constants ◽  
Gauge Symmetries ◽  
Gauge Fixing ◽  
Definition Of

In this paper, we explore the possibility of constructing the quantum chromodynamics of a massive color-octet vector field without introducing higher structures like extended gauge symmetries, extra dimensions or scalar fields. We show that gauge invariance is not enough to constraint the couplings. Nevertheless, the requirement of unitarity fixes the values of the coupling constants, which otherwise would be arbitrary. Additionally, it opens a new discrete symmetry which makes the coloron stable and avoid its resonant production at a collider. On the other hand, a judicious definition of the gauge fixing terms modifies the propagator of the massive field making it well-behaved in the ultraviolet limit. The relation between our model and the more general approach based on extended gauge symmetries is also discussed.

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