相关论文: Discretization, Moyal, and integrability
We give a q-analysis version of a discretization procedure of Kemmoku and Saito leading to an apparently new q-Moyal type bracket.
The Moyal quantization is described as a discretization of the classical phase space by using difference analogue of vector fields. Difference analogue of Lie brackets plays the role of Heisenberg commutators.
Quantization of BKP type equations are done through the Moyal bracket and the formalism of pseudo-differential operators. It is shown that a variant of the dressing operator can also be constructed for such quantized systems.
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…
We show how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic groupoid…
We deduce a kernel that allows the Moyal quantization of the cylinder (as phase space) by means of the Stratonovich-Weyl correspondence.
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the…
Following the techniques of M. Sato (see \cite{Sa}), a generalization of the KP hierarchy for more than one variable is proposed. An approach to the classification of solutions and a method to construct algebraic solutions is also offered.
An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…
The relation between the Moyal-Weyl deformation quantization and quasiconformal mappings of Riemann surfaces of complex analysis are shown by several examples.
Moyal-deformed hierarchies of soliton equations can be extended to larger hierarchies by including additional evolution equations with respect to the deformation parameters. A general framework is presented in which the extension is…
A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently.…
A $\bar{\partial}$-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane are described and some clases of explicit solutions of the…
We discuss the phase structure and thermodynamics of QCD by means of dynamical chiral effective models. Quark and meson fluctuations are included via the functional renormalization group. We study the influence of confinement in addition to…
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are…
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.
A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an…
Nonlinear optical media of Kerr type are described by a particular version of an anharmonic quantum harmonic oscillator. The dynamics of this system can be described using the Moyal equations of motion, which correspond to a quantum phase…