Comment on the Geometric Interpretation of Ito Calculus on a Lattice | Zendy

N. Nakazawa | Zendy

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Comment on the Geometric Interpretation of Ito Calculus on a Lattice

Author(s) -

N. Nakazawa

Publication year - 2003

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.110.393

Subject(s) - stochastic quantization , physics , covariant transformation , langevin equation , mathematical physics , interpretation (philosophy) , gauge theory , quantum stochastic calculus , lattice (music) , lattice field theory , stochastic interpretation , quantization (signal processing) , classical mechanics , theoretical physics , quantum mechanics , mathematics , quantum , path integral formulation , quantum process , computer science , acoustics , quantum dynamics , programming language , algorithm

A covariant nature of the Langevin equation in Ito calculus is clarified inapplying stochastic quantization method to U(N) and SU(N) lattice gaugetheories. The stochastic process is expressed in a manifestly generalcoordinate covariant form as a collective field theory on the group manifold. Ageometric interpretation is given for the Langevin equation and thecorresponding Fokker-Planck equation in the sense of Ito.Comment: 9 page

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