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 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 Finite field-dependent symmetry in the Thirring model

2016 ◽  
Vol 2016 (6) ◽  
pp. 063B04 ◽  
Author(s):  
Sudhaker Upadhyay ◽  
Prince A. Ganai
Keyword(s):  
Finite Field ◽  
Thirring Model ◽  
Field Dependent

Finite field-dependent BRS transformation and axial gauges

2000 ◽  
Vol 33 (33) ◽  
pp. 5951-5951
Author(s):  
R S Bandhu ◽  
S D Joglekar
Keyword(s):  
Finite Field ◽  
Field Dependent

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.

APPLICATION OF FINITE FIELD-DEPENDENT BRS TRANSFORMATIONS TO PROBLEMS OF THE COULOMB GAUGE

2002 ◽  
Vol 17 (09) ◽  
pp. 1279-1299 ◽  
Author(s):  
SATISH D. JOGLEKAR ◽  
BHABANI PRASAD MANDAL
Keyword(s):  
Finite Field ◽  
Path Integral ◽  
Ad Hoc ◽  
High Energy ◽  
Coulomb Gauge ◽  
Gauge Parameter ◽  
Path Integral Formulation ◽  
High Energy Behavior ◽  
Energy Behavior ◽  
Field Dependent

We discuss the Coulomb propagator in the formalism developed recently in which we construct the Coulomb gauge path-integral by correlating it with the well-defined Lorentz gauge path-integrals through a finite field-dependent BRS transformation. We discover several features of the Coulomb gauge from it. We find that the singular Coulomb gauge has to be treated as the gauge parameter λ → 0 limit. We further find that the propagator so obtained has good high energy behavior[Formula: see text] for λ ≠ 0 and ∊ ≠ 0. We also find that the behavior of the propagator so obtained is sensitive to the order of limits k0→ ∞, λ → 0 and ∊ → 0; so that these have to be handled carefully in a higher loop calculation. We show that we can arrive at the result of Cheng and Tsai for the ambiguous two-loop Feynman integrals without the need for an extra ad hoc regularization and within the path integral formulation.

scholarly journals CORRECT TREATMENT OF $\bm{{1\over (\eta\cdot{\lc{k}})^{\lc{p}}}}$ SINGULARITIES IN THE AXIAL GAUGE PROPAGATOR

2000 ◽  
Vol 15 (10) ◽  
pp. 1453-1479 ◽  
Author(s):  
SATISH D. JOGLEKAR ◽  
A. MISRA
Keyword(s):  
Finite Field ◽  
Path Integral ◽  
Small Region ◽  
Alternative Procedure ◽  
Complicated Structure ◽  
Integral Formalism ◽  
Correct Treatment ◽  
Text Type ◽  
Axial Gauge ◽  
Field Dependent

The propagators in axial-type, light-cone and planar gauges contain [Formula: see text]-type singularities. These singularities have generally been treated by inventing prescriptions for them. In this work, we propose an alternative procedure for treating these singularities in the path integral formalism using the known way of treating the singularities in Lorentz gauges. To this end, we use a finite field-dependent BRS transformation that interpolates between Lorentz-type and the axial-type gauges. We arrive at the ε-dependent tree propagator in the axial-type gauges. We examine the singularity structure of the propagator and find that the axial gauge propagator so constructed has no spurious poles (for real k). It however has a complicated structure in a small region near η·k=0. We show how this complicated structure can effectively be replaced by a much simpler propagator.

scholarly journals THE NONCOVARIANT GAUGES IN 3-FORM THEORIES

2013 ◽  
Vol 28 (10) ◽  
pp. 1350033 ◽  
Author(s):  
SUDHAKER UPADHYAY ◽  
MANOJ KUMAR DWIVEDI ◽  
BHABANI PRASAD MANDAL
Keyword(s):  
Gauge Theory ◽  
Finite Field ◽  
Brst Symmetry ◽  
Generating Functional ◽  
Field Dependent ◽  
Covariant Gauge

We study the 3-form gauge theory in the context of generalized BRST formulation. We construct the finite field-dependent BRST symmetry for such a theory. The generating functional for 3-form gauge theory in noncovariant gauge is obtained from that of covariant gauge. We further extend the results by considering 3-form gauge theory in the context of Batalin–Vilkovisky formulation.

Finite field-dependent BRS transformation and axial gauges

1998 ◽  
Vol 31 (18) ◽  
pp. 4217-4224 ◽  
Author(s):  
Rudra Shyam Bandhu ◽  
Satish D Joglekar
Keyword(s):  
Finite Field ◽  
Field Dependent
Sign in / Sign up

Export Citation Format

Share Document