ON THE ROLE OF WIGNER'S LITTLE GROUP AS A GENERATOR OF GAUGE TRANSFORMATION IN MAXWELL–CHERN–SIMONS THEORY

2001 ◽  
Vol 16 (13) ◽  
pp. 853-862 ◽  
Author(s):  
RABIN BANERJEE ◽  
BISWAJIT CHAKRABORTY ◽  
TOMY SCARIA
Keyword(s):  
Gauge Transformation ◽  
Simons Theory ◽  
Temporal Gauge ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

The role of Wigner's little group in 2 + 1 dimensions as a generator of gauge transformation in the topologically massive Maxwell–Chern–Simons (MCS) theory is discussed. The similarities and dissimilarities between the Maxwell and MCS theories in the context of gauge fixing (spatial transversality and temporal gauge) are also analyzed.

scholarly journals Quantum double and κ-Poincaré symmetries in (2+1)-gravity and Chern–Simons theoryThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 245-250
Author(s):  
C. Meusburger
Keyword(s):  
Hopf Algebra ◽  
Simons Theory ◽  
De Sitter ◽  
Quantum Double ◽  
Isometry Groups ◽  
Chern Simons ◽  
Chern Simons Theory

We clarify the role of Drinfeld doubles and κ-Poincaré symmetries in quantized (2+1)-gravity and Chern–Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern–Simons theory and determine this compatibility explicitly for the Drinfeld doubles and κ-Poincaré symmetries associated with the isometry groups of (2+1)-gravity. In particular, we show that κ-Poincaré symmetries with a timelike deformation are not directly associated with (2+1)-gravity. The association between these κ-Poincaré symmetries and Chern–Simons theory is possible only in the de Sitter case and the relevant Chern–Simons theory is physically inequivalent to (2+1)-gravity.

scholarly journals A GENERAL SOLUTION OF THE BV-MASTER EQUATION AND BRST FIELD THEORIES

1993 ◽  
Vol 08 (22) ◽  
pp. 2087-2097 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
Master Equation ◽  
General Procedure ◽  
Field Theories ◽  
Simons Theory ◽  
Proper Solution ◽  
First Order ◽  
Brst Charge ◽  
Chern Simons ◽  
Chern Simons Theory

For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories when one replaces the role of the exterior derivative with the BRST charge of first quantization.

scholarly journals Higher spin Chern–Simons theory and the super Boussinesq hierarchy

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1850085
Author(s):  
Michael Gutperle ◽  
Yi Li
Keyword(s):  
Time Evolution ◽  
Gauge Transformation ◽  
Poisson Structure ◽  
Higher Spin Gravity ◽  
Hamiltonian Structure ◽  
Evolution Equations ◽  
Simons Theory ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper, we construct a map between a solution of supersymmetric Chern–Simons higher spin gravity based on the superalgebra [Formula: see text] with Lifshitz scaling and the [Formula: see text] super Boussinesq hierarchy. We show that under this map the time evolution equations of both theories coincide. In addition, we identify the Poisson structure of the Chern–Simons theory induced by gauge transformation with the second Hamiltonian structure of the super Boussinesq hierarchy.

scholarly journals On higher holonomy invariants in higher gauge theory I

2016 ◽  
Vol 13 (07) ◽  
pp. 1650090 ◽  
Author(s):  
Roberto Zucchini
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Simons Theory ◽  
Arbitrary Genus ◽  
Higher Gauge Theory ◽  
Chern Simons ◽  
Base Data ◽  
Chern Simons Theory

This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern–Simons theory. For a flat 2-connection, we define the 2-holonomy of surface knots of arbitrary genus and determine its covariance properties under 1-gauge transformation and change of base data.

CHERN–SIMONS THEORY, HIDA DISTRIBUTIONS, AND STATE MODELS

2003 ◽  
Vol 06 (supp01) ◽  
pp. 65-81 ◽  
Author(s):  
S. ALBEVERIO ◽  
A. HAHN ◽  
A. N. SENGUPTA
Keyword(s):  
Wilson Loop ◽  
Functional Integral ◽  
Simons Theory ◽  
Infinite Dimensional ◽  
Linking Number ◽  
Gauge Fixing ◽  
Regularization Techniques ◽  
State Models ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we present the central ideas and results of a rigorous theory of the Chern–Simons functional integral. In particular, we show that it is possible to define the Wilson loop observables (WLOs) for pure Chern–Simons models with base manifold M = ℝ3 rigorously as infinite dimensional oscillatory integrals by exploiting an "axial gauge fixing" and applying certain regularization techniques like "loop-smearing" and "framing". The (values of the) WLOs can be computed explicitly. If the structure group G of the model is Abelian one obtains well-known linking number expressions for the WLOs. If G is Non-Abelian one obtains expressions which are similar but not identical to the state model representations for the Homfly and Kauffman polynomials given in [19, 21, 31].

scholarly journals On the Quantization of Isomonodromic Deformations on the Torus

1997 ◽  
Vol 12 (11) ◽  
pp. 2013-2029 ◽  
Author(s):  
D. Korotkin ◽  
H. Samtleben
Keyword(s):  
Poisson Bracket ◽  
Poisson Structure ◽  
Hamiltonian Formulation ◽  
Simons Theory ◽  
Isomonodromic Deformation ◽  
Isomonodromic Deformations ◽  
Gauge Fixing ◽  
Meromorphic Connection ◽  
Chern Simons ◽  
Chern Simons Theory

The quantization of isomonodromic deformation of a meromorphic connection on the torus is shown to lead directly to the Knizhnik–Zamolodchikov–Bernard equations in the same way as the problem on the sphere leads to the system of Knizhnik–Zamolodchikov equations. The Poisson bracket required for a Hamiltonian formulation of isomonodromic deformations is naturally induced by the Poisson structure of Chern–Simons theory in a holomorphic gauge fixing. This turns out to be the origin of the appearance of twisted quantities on the torus.

Hamiltonian, path integral, and BRST formulations of the Chern–Simons theory under appropriate gauge-fixing

2008 ◽  
Vol 86 (2) ◽  
pp. 401-407 ◽  
Author(s):  
U Kulshreshtha ◽  
D S Kulshreshtha
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Simons Theory ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

The Hamiltonian, path integral, and BRST formulations of the Chern–Simons theory in two-space one-time dimensions are investigated under appropriate gauge-fixing conditions.PACS Nos.: 11.10.Ef, 11.10.Kk, 12.20.Ds

scholarly journals Geometric aspects of interpolating gauge-fixing in Chern–Simons theory

2018 ◽  
Vol 33 (02) ◽  
pp. 1850012
Author(s):  
Laurent Gallot ◽  
Philippe Mathieu ◽  
Éric Pilon ◽  
Frank Thuillier
Keyword(s):  
Simons Theory ◽  
3 Dimensional ◽  
Linking Number ◽  
Gauge Fixing ◽  
Covariant Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we investigate an interpolating gauge-fixing procedure in (4l + 3)-dimensional Abelian Chern–Simons theory. We show that this interpolating gauge is related to the covariant gauge in a constant anisotropic metric. We compute the corresponding propagators involved in various expressions of the linking number in various gauges. We comment on the geometric interpretations of these expressions, clarifying how to pass from one interpretation to another.

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