Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems
Year: 1997
Type: article
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.
DOI: 10.1143/jpsj.66.51
Author: Ryuji Kemmoku
Institution: Tokyo Metropolitan University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2091264074