dorsal/arxiv
View SchemaDifference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems
| Authors | Ryuji Kemmoku |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9612005 |
| URL | https://arxiv.org/abs/solv-int/9612005 |
| DOI | 10.1143/JPSJ.66.51 |
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.
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"abstract": "Inspired by the fact that the Moyal quantization is related with nonlocal\noperation, I define a difference analogue of vector fields and rephrase quantum\ndescription on the phase space. Applying this prescription to the theory of the\nKP-hierarchy, I show that their integrability follows to the nature of their\nWigner distribution. Furthermore the definition of the ``expectation value\u0027\u0027\nclarifies the relation between our approach and the Hamiltonian structure of\nthe KP-hierarchy. A trial of the explicit construction of the Moyal bracket\nstructure in the integrable system is also made.",
"arxiv_id": "solv-int/9612005",
"authors": [
"Ryuji Kemmoku"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1143/JPSJ.66.51",
"title": "Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems",
"url": "https://arxiv.org/abs/solv-int/9612005"
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