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Prog. Theor. Phys. Supplement No.111 (1993) pp. 373-388

[ Full Text PDF : FREE ACCESS (1040K) ]

Stochastic Quantization of Topological Field Theory

Yong-Shi Wu and Chuan-Jie Zhu

Physics Department, University of Utah, Salt Lake City, Utah 84112, U.S.A.

Abstract:

A Euclidean topological action is always purely imaginary; its stochastic quantization inevitably involves the complex Langevin equation. We show that the standard results for abelian Chern-Simons they can be reproduced in the stochastic approach with the Maxwell terms as a regularization; but if one ignores the factor of i, the Langevin equation will become pathological. Simplification may occur if one uses the generalized Langevin equation with an appropriate, purely imaginary kernel; we exemplify this by stochastic quantization in Minkowski space-time and again the abelian Chern-Simons theory. The stochastic perturbation theory of non-abelian Chern-Simons theory is also studied and the contributions of usual Faddeev-Popov ghosts are verified to be reproducible without gauge fixing.


URL : http://ptp.ipap.jp/link?PTPS/111/373/
DOI : 10.1143/PTPS.111.373

[ Full Text PDF : FREE ACCESS (1040K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 92 No. 6 (1994) pp. 1185-1205 :
    Stochastic Quantization of the Non-Abelian Chern-Simons Gauge Theory Based on a Kerneled Lagevin Equation and Faddeev-Popov Ghost Effects
    Masashi Mizutani and Ichiro Ohba

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