Noncommutative Differential Calculus on Discrete Abelian Groups and Its Applications*

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? International Academic Publishers
, , Citation Guo HanYing et al 2000 Commun. Theor. Phys. 34 245 DOI 10.1088/0253-6102/34/2/245

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Author affiliations

1 Institute of Theoretical Physics, Academia Sinica, P.O. Box 2735, Beijing 100080, china

2 Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009(26), Beijing 100088, China

Dates

  1. Received 8 September 1999
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0253-6102/34/2/245

Abstract

A new noncommutative differential calculus on function space of discrete Abelian groups is proposed. The derivatives are introduced with respect to the generators of the groups only. It is applied to discrete symplectic geometry and Hamiltonian systems with $H(p, q) = T(p) + V(q)$ as well as the lattice gauge theory on regular lattice.

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  • * 

10.1088/0253-6102/34/2/245