scholarly journals On the BRST and finite field-dependent BRST of a model where vector and axial vector interactions get mixed up with different weights

2016 ◽  
Vol 31 (32) ◽  
pp. 1650171 ◽  
Author(s):  
Safia Yasmin ◽  
Anisur Rahaman
Keyword(s):  
Gauge Symmetry ◽  
Finite Field ◽  
Axial Vector ◽  
Dimensional Model ◽  
Brst Transformation ◽  
Gauge Invariant ◽  
Local Gauge Symmetry ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Lower Dimensional

The generalized version of a lower dimensional model where vector and axial vector interactions get mixed up with different weights is considered. The bosonized version of which does not possess the local gauge symmetry. An attempt has been made here to construct the BRST invariant reformulation of this model using Batalin–Fradlin and Vilkovisky formalism. It is found that the extra field needed to make it gauge invariant turns into Wess–Zumino scalar with appropriate choice of gauge fixing. An application of finite field-dependent BRST and anti-BRST transformation is also made here in order to show the transmutation between the BRST symmetric and the usual nonsymmetric version of the model.

scholarly journals CONNECTING GREEN FUNCTIONS IN AN ARBITRARY PAIR OF GAUGES AND AN APPLICATION TO PLANAR GAUGES

2001 ◽  
Vol 16 (31) ◽  
pp. 5043-5059 ◽  
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Green Function ◽  
Finite Field ◽  
Path Integrals ◽  
Green Functions ◽  
Expectation Values ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Field Dependent ◽  
Gauge Connection ◽  
Arbitrary Gauge

We establish a finite field-dependent BRS transformation that connects the Yang–Mills path integrals with the Faddeev–Popov effective actions for an arbitrary pair of gauges F and F'. We establish a result that relates an arbitrary Green function (either a primary one or that of an operator) in an arbitrary gauge F' to those in gauge F that are compatible to the ones in gauge Fby its construction. This is because the construction preserves expectation values of gauge-invariant observables. We establish parallel results also for the planar gauge-Lorentz gauge connection.

scholarly journals Double Hodge Theory for a Particle on Torus

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Vipul Kumar Pandey ◽  
Bhabani Prasad Mandal
Keyword(s):  
Finite Field ◽  
Hodge Theory ◽  
Toric Geometry ◽  
Brst Transformation ◽  
Mathematical Properties ◽  
Field Dependent ◽  
Finite Transformation

We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.

scholarly journals A systematic study of finite field-dependent BRST-BV transformations in Sp(2) extended field–antifield formalism

2014 ◽  
Vol 29 (29) ◽  
pp. 1450167 ◽  
Author(s):  
Igor A. Batalin ◽  
Klaus Bering ◽  
Peter M. Lavrov ◽  
Igor V. Tyutin
Keyword(s):  
Finite Field ◽  
Path Integral ◽  
Systematic Study ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Extended Field

In the framework of Sp(2) extended Lagrangian field–antifield BV formalism, we study systematically the role of finite field-dependent BRST-BV transformations. We have proved that the Jacobian of a finite BRST-BV transformation is capable of generating arbitrary finite change of the gauge-fixing function in the path integral.

scholarly journals Quantum gauge symmetry from finite field dependent BRST transformations

2000 ◽  
Vol 488 (1) ◽  
pp. 27-30 ◽  
Author(s):  
Rabin Banerjee ◽  
Bhabani Prasad Mandal
Keyword(s):  
Gauge Symmetry ◽  
Finite Field ◽  
Field Dependent

scholarly journals QUANTUM AND CLASSICAL GAUGE SYMMETRIES IN A MODIFIED QUANTIZATION SCHEME

2001 ◽  
Vol 16 (10) ◽  
pp. 1775-1788 ◽  
Author(s):  
KAZUO FUJIKAWA ◽  
HIROAKI TERASHIMA
Keyword(s):  
Gauge Symmetry ◽  
Brst Symmetry ◽  
Mass Term ◽  
Large Mass ◽  
Quantization Scheme ◽  
Mass Limit ◽  
Classical Action ◽  
Gauge Invariant ◽  
Gauge Fixing ◽  
Nonlinear Gauge

The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the nonlinear gauge [Formula: see text] of Dirac and Nambu in the large mass limit. We have recently shown that this modified quantization scheme is in fact identical to the conventional local Faddeev–Popov formula without taking the large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit and if the Gribov complications can be ignored. This suggests that the classical massive vector theory, for example, is interpreted in a more flexible manner either as a gauge invariant theory with a gauge fixing term added, or as a conventional massive nongauge theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge-invariant, has a more intrinsic meaning. It is suggested that we extend the notion of quantum gauge symmetry (BRST symmetry) not only to classical gauge theory but also to a wider class of theories whose gauge symmetry is broken by some extra terms in the classical action. We comment on the implications of this extended notion of quantum gauge symmetry.

scholarly journals WILSON LOOP AND THE TREATMENT OF AXIAL GAUGE POLES

2000 ◽  
Vol 15 (08) ◽  
pp. 541-546 ◽  
Author(s):  
SATISH. D. JOGLEKAR ◽  
A. MISRA
Keyword(s):  
Finite Field ◽  
Wilson Loop ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Gauge Invariant ◽  
Expectation Value ◽  
Direct Verification ◽  
Axial Gauge ◽  
Field Dependent ◽  
New Treatment

We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that under the FFBRS transformation as the vacuum expectation value of a gauge-invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Furthermore, we give an argument for direct verification of the invariance of Wilson loop to O(g4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wilson loop to O(g2).

scholarly journals Finite BRST–BFV transformations for dynamical systems with second-class constraints

2015 ◽  
Vol 30 (21) ◽  
pp. 1550108 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov ◽  
Igor V. Tyutin
Keyword(s):  
Dynamical Systems ◽  
Finite Field ◽  
Path Integral ◽  
Hamiltonian Formalism ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Compensation Equation

We study finite field-dependent BRST–BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

One-loop divergences in anomaly-free non-Abelian axial models

2003 ◽  
Vol 81 (12) ◽  
pp. 1343-1347
Author(s):  
M P Gagné-Portelance ◽  
D.G.C. McKeon
Keyword(s):  
Axial Vector ◽  
Invariant Operator ◽  
Diagonal Element ◽  
Dimensional Model ◽  
Vector Coupling ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Left Handed ◽  
Axial Vector Coupling ◽  
The Matrix

We consider one-loop divergences in a four-dimensional model in which a non-Abelian vector field has an axial vector coupling with a massless left-handed spinor field. This is done by computing the diagonal element of the second Seeley–deWitt coefficient a2(x,x). Even when the coupling is such that the axial anomaly vanishes, divergences arise that are not gauge invariant. Operator regularization is used throughout so as to leave the matrix γ5 unambiguously defined. PACS No.: 11.15.q

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

Sign in / Sign up

Export Citation Format

Share Document