scholarly journals Gauge-fixing, semiclassical approximation and potentials for graded Chern-Simons theories

2002 ◽  
Vol 2002 (03) ◽  
pp. 022-022 ◽  
Author(s):  
Calin I Lazaroiu ◽  
Radu Roiban
Keyword(s):  
Semiclassical Approximation ◽  
Gauge Fixing ◽  
Chern Simons

GAUGE FIXING AND QUANTUM GROUP SYMMETRIES IN (2+1)-GRAVITY

2013 ◽  
Vol 10 (08) ◽  
pp. 1360004
Author(s):  
CATHERINE MEUSBURGER ◽  
TORSTEN SCHÖNFELD
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
Baxter Equation ◽  
Poisson Structures ◽  
R Matrix ◽  
Point Particles ◽  
Combinatorial Description ◽  
Gauge Fixing ◽  
Group Symmetries ◽  
Chern Simons

We summarize the results obtained by applying Dirac's gauge fixing formalism to the combinatorial description of the Chern–Simons formulation of (2+1)-gravity and their implications for the symmetries of the quantum theory. While the combinatorial description of the phase space exhibits standard Poisson–Lie symmetries, every gauge fixing condition based on two point particles yields a Poisson structure determined by a dynamical classical r-matrix. By considering transformations between different gauge fixing conditions, it is possible to classify all gauge fixed Poisson structures in terms of two standard solutions of the dynamical classical Yang–Baxter equation. We discuss the conclusions that can be drawn from this about the symmetries of (2+1)-dimensional quantum gravity.

Topological Invariance of Fractional Spin of the Abelian CSH Vortex

1997 ◽  
Vol 12 (13) ◽  
pp. 2343-2359 ◽  
Author(s):  
Ashim Kumar Roy
Keyword(s):  
Topological Charge ◽  
Contradictory Result ◽  
Fractional Spin ◽  
Shape Dependence ◽  
Careful Scrutiny ◽  
Gauge Fixing ◽  
Explicit Analysis ◽  
Vortex Solutions ◽  
Topological Invariance ◽  
Chern Simons

The Abelian Chern–Simons–Higgs model in 2 + 1 dimensions exhibit vortex solutions with fractional spin. Although it is known that the normal, underformed charged vortex has a fractional spin related to its topological charge, it is not clear whether the value of this fractional spin is stable under changes in gauge-fixing conditions and regular deformations of the vortex field configurations. Recently, some authors have reported about the gauge as well as shape dependence of the fractional spin for the CSH vortex, which is contrary to our usual belief. However, their analysis is inconsistent and calls for a careful scrutiny. An explicit analysis is presented in this paper to show that the fractional spin for the Abelian CSH charged vortex may indeed be taken to be a gauge (small) and shape independent and hence, a topologically invariant quantity. The subtle points missed out by the other authors leading to inconsistency and the contradictory result are discussed in all essential details to resolve the issue.

scholarly journals EFFECTIVE POTENTIAL FOR A NONRELATIVISTIC NON-ABELIAN CHERN-SIMONS MATTER SYSTEM IN CONSTANT BACKGROUND FIELDS

1995 ◽  
Vol 10 (29) ◽  
pp. 4187-4201
Author(s):  
DIDIER CAENEPEEL ◽  
MARTIN LEBLANC
Keyword(s):  
Effective Potential ◽  
Conformal Symmetry ◽  
Functional Method ◽  
Coupling Constant ◽  
Gauge Fixing ◽  
Matter System ◽  
Background Fields ◽  
Aharonov Bohm ◽  
Chern Simons ◽  
Matter Sector

We present the effective potential for nonrelativistic matter coupled to non-Abelian Chern-Simons gauge fields. We perform the calculation using a functional method in constant background fields to satisfy Gauss’s law and to simplify the computation. Both the quantum gauge and matter fields are integrated over. The gauge-fixing is achieved with an Rξ gauge in the ξ→0 limit. Divergences appearing in the matter sector are regulated via operator regularization. We find no correction to the Chern-Simons coupling constant and the system experiences conformal symmetry breaking to one-loop order except at the known value of self-duality. These results agree with previous analysis of the non-Abelian Aharonov-Bohm scattering.

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

2009 ◽  
Vol 79 (4) ◽  
pp. 045001 ◽  
Author(s):  
Usha Kulshreshtha ◽  
D S Kulshreshtha ◽  
H J W Mueller-Kirsten ◽  
J P Vary
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Gauge Fixing ◽  
Chern Simons

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 TORSION ON HYPERBOLIC MANIFOLDS AND THE SEMICLASSICAL LIMIT FOR CHERN–SIMONS THEORY

1998 ◽  
Vol 13 (30) ◽  
pp. 2453-2461 ◽  
Author(s):  
A. A. BYTSENKO ◽  
A. E. GONÇALVES ◽  
W. DA CRUZ
Keyword(s):  
Integration Method ◽  
Semiclassical Approximation ◽  
Semiclassical Limit ◽  
Hyperbolic Manifolds ◽  
Simons Theory ◽  
Manifold With Boundary ◽  
Hyperbolic Three Manifolds ◽  
Chern Simons ◽  
Chern Simons Theory ◽  
Invariant Integration

The invariant integration method for Chern–Simons theory of gauge group SU(2) and manifold Γ\H3 is verified in the semiclassical limit. The semiclassical approximation for the partition function associated with a connected sum of hyperbolic three-manifolds is presented. We discuss briefly L2-analytical and topological torsions of a manifold with boundary.

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