Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems
solv-int
2009-10-30 v1 Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.solv-int/9612005,
title = {Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems},
author = {Ryuji Kemmoku},
journal= {arXiv preprint arXiv:solv-int/9612005},
year = {2009}
}
Comments
19 pages, to appear in J. Phys. Soc. Jpn