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

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

1996-12-11

arxiv.org/abs/solv-int/9612005v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1143/JPSJ.66.51

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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