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Comment on Geometric Interpretation of Ito Calculus on the Lattice

Naohito Nakazawa
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Abstract

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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Naohito Nakazawa. 2003-03-02. Comment on Geometric Interpretation of Ito Calculus on the Lattice. https://doi.org/10.1143/ptp.110.393

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