Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral

A genuinely three-dimensional covariant approach to the monodromy operator (skein relations) in the context of Chern-Simons theory is proposed. A holomorphic path-integral representation for the holonomy operator (Wilson loop) and for the non-abelian Stokes theorem is used.

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FRACTIONAL STATISTICS INDUCED BY GAUGE FIELDS

Modern Physics Letters A ◽

10.1142/s0217732391000385 ◽

1991 ◽

Vol 06 (05) ◽

pp. 391-398 ◽

Cited By ~ 1

Author(s):

ASHOK CHATTERJEE ◽

V.V. SREEDHAR

Keyword(s):

Gauge Theory ◽

Gauge Field ◽

Path Integral ◽

Simple Proof ◽

Scalar Particle ◽

Gauge Fields ◽

Fractional Statistics ◽

Chern Simons

An explicit extension of Polyakov’s analysis of a scalar particle coupled to an Abelian Chern-Simons gauge theory to the case of two particles and arbitrary values of the coupling is given. A simple proof of the emergence of fractional statistics induced by the gauge field follows within the path-integral framework.

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NON-ABELIAN GAUGE THEORY FOR CHERN–SIMONS PATH INTEGRAL ON R3

Journal of Knot Theory and Its Ramifications ◽

10.1142/s021821651100987x ◽

2012 ◽

Vol 21 (04) ◽

pp. 1250039 ◽

Cited By ~ 5

Author(s):

ADRIAN P. C. LIM

Keyword(s):

Gauge Theory ◽

Gauge Group ◽

Path Integral ◽

Wilson Loop ◽

Wiener Measure ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Chern Simons

In a prequel to this article, we used abstract Wiener measure to define the Chern–Simons path integral over ℝ3. In this sequel, we compute the Wilson Loop observable for the non-abelian gauge group and compare with current knot literature.

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

Physica Scripta ◽

10.1088/0031-8949/82/05/055101 ◽

2010 ◽

Vol 82 (5) ◽

pp. 055101 ◽

Cited By ~ 6

Author(s):

U Kulshreshtha ◽

D S Kulshreshtha ◽

J P Vary

Keyword(s):

Path Integral ◽

Hamiltonian Path ◽

Light Front ◽

Gauge Fixing ◽

Chern Simons

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QuantumSO(3)-invariants dominate theSU(2)-invariant of Casson and Walker

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100073084 ◽

1995 ◽

Vol 117 (2) ◽

pp. 237-249 ◽

Cited By ~ 25

Author(s):

Hitoshi Murakami

Keyword(s):

Path Integral ◽

Lie Group ◽

Mathematical Proof ◽

Topological Invariants ◽

Compact Lie Group ◽

Feynman Path Integral ◽

Feynman Path ◽

Chern Simons

For a compact Lie groupG, E. Witten proposed topological invariants of a threemanifold (quantumG-invariants) in 1988 by using the Chern-Simons functional and the Feynman path integral [30]. See also [2]. N. Yu. Reshetikhin and V. G. Turaev gave a mathematical proof of existence of such invariants forG=SU(2) [28]. R. Kirby and P. Melvin found that the quantumSU(2)-invariantassociated toq= exp(2π √ − 1/r) withrodd splits into the product of the quantumSO(3)-invariantand[15]. For other approaches to these invariants, see [3, 4, 5, 16, 22, 27].

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