scholarly journals ANOMALOUS CHIRAL ACTION FROM THE PATH INTEGRAL

1998 ◽  
Vol 13 (04) ◽  
pp. 523-551 ◽  
Author(s):  
M. M. ISLAM ◽  
S. J. PUGLIA
Keyword(s):  
Gauge Field ◽  
Path Integral ◽  
Proper Time ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Splitting Technique ◽  
Left Handed ◽  
Consistency Requirement ◽  
Point Splitting ◽  
Anomalous Theory

By generalizing the Fujikawa approach, we show in the path integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern–Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. We consider a massless left-handed fermion interacting with a non-Abelian gauge field. The gauge field also interacts with a set of Goldstone bosons, so that a gauge-invariant configuration of the gauge field exists. We use Schwinger's "proper time" representation of the Green's function and the guage-invariant point-splitting technique, and find that the consistency requirement and the point-splitting technique allow both an anomalous and a nonanomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory or a nonanomalous theory.

scholarly journals Dirac Particle in External Non-Abelian Gauge Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bilel Hamil ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Gauge Field ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Formalism ◽  
Abelian Gauge ◽  
Lorentz Gauge ◽  
Path Integral Formalism ◽  
The Green Function

The Green function of a Dirac particle in interaction with a non-Abelian SU(N) gauge field exactly and analytically determined via the path integral formalism by using the approach so-called “global projection.” The essential steps in the calculation are the choice of a convenient gauge (Lorentz gauge) and the introduction of two constraints, φ=kx (related to space) and Grassmannian η=kψ (related to Dirac matrices). Furthermore, it is shown that certain selected equations obtained during the integrations can also be classically derived.

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.

scholarly journals CONSTRAINED DYNAMICS OF THE COUPLED ABELIAN TWO-FORM

1993 ◽  
Vol 08 (25) ◽  
pp. 2403-2412 ◽  
Author(s):  
AMITABHA LAHIRI
Keyword(s):  
Phase Space ◽  
Gauge Field ◽  
Antisymmetric Tensor ◽  
Abelian Gauge ◽  
Constrained Dynamics ◽  
Duality Transformations ◽  
Tensor Potential

I present the reduction of phase space of the theory of an antisymmetric tensor potential coupled to an Abelian gauge field, using Dirac's procedure. Duality transformations on the reduced phase space are also discussed.

scholarly journals Gauge inflation by kinetic coupled gravity

2014 ◽  
Vol 29 (30) ◽  
pp. 1450161 ◽  
Author(s):  
F. Darabi ◽  
A. Parsiya
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Einstein Tensor ◽  
Abelian Gauge ◽  
Metric Tensor ◽  
New Class ◽  
Slow Roll ◽  
Set Up ◽  
Inflationary Models

Recently, a new class of inflationary models, so-called gauge-flation or non-Abelian gauge field inflation has been introduced where the slow-roll inflation is driven by a non-Abelian gauge field A with the field strength F. This class of models are based on a gauge field theory having F2 and F4 terms with a non-Abelian gauge group minimally coupled to gravity. Here, we present a new class of such inflationary models based on a gauge field theory having only F2 term with non-Abelian gauge fields non-minimally coupled to gravity. The non-minimal coupling is set up by introducing the Einstein tensor besides the metric tensor within the F2 term, which is called kinetic coupled gravity. A perturbation analysis is performed to confront the inflation under consideration with Planck and BICEP2 results

scholarly journals Inflationary dynamics with a non-Abelian gauge field

2013 ◽  
Vol 87 (2) ◽  
Author(s):  
Kei-ichi Maeda ◽  
Kei Yamamoto
Keyword(s):  
Gauge Field ◽  
Abelian Gauge
Sign in / Sign up

Export Citation Format

Share Document