vix.ing · top · new · best · stats · spec

Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems

1996/12/11 by Ryuji Kemmoku
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #nlin.SI #solv-int

paper · pdf · doi:10.1143/jpsj.66.51

19 pages, to appear in J. Phys. Soc. Jpn

arxiv created 1996/12/11 · openalex publication_date 1997/01/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this prescription to the theory of the KP-hierarchy, I show that their integrability follows to the nature of their Wigner distribution. Furthermore the definition of the ``expectation value'' clarifies the relation between our approach and the Hamiltonian structure of the KP-hierarchy. A trial of the explicit construction of the Moyal bracket structure in the integrable system is also made.

Citations