Comment on Geometric Interpretation of Ito Calculus on the Lattice

Details Comment on Geometric Interpretation of Ito Calculus on the Lattice Comment on Geometric Interpretation of Ito Calculus on the Lattice

2003-03-02

arxiv.org/abs/hep-th/0303004v1

Prog.Theor.Phys. 110 (2003) 393-398

Physics

High Energy Physics

High Energy Physics - Theory

9 pages

Scientific paper

10.1143/PTP.110.393

A covariant nature of the Langevin equation in Ito calculus is clarified in applying stochastic quantization method to U(N) and SU(N) lattice gauge theories. The stochastic process is expressed in a manifestly general coordinate covariant form as a collective field theory on the group manifold. A geometric interpretation is given for the Langevin equation and the corresponding Fokker-Planck equation in the sense of Ito.

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