# DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE

@article{Zachos2002DEFORMATIONQQ, title={DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE}, author={C. Zachos}, journal={International Journal of Modern Physics A}, year={2002}, volume={17}, pages={297-316} }

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (e.g. quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a… Expand

#### 146 Citations

Deformation quantization of noncommutative quantum mechanics

- Physics
- 2004

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper,… Expand

Deformation quantization of geometric quantum mechanics

- Mathematics, Physics
- 2002

Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schr¨ odinger spinless field is considered. Under the assumption that the phase space of… Expand

Quantum field theory in phase space

- Physics
- International Journal of Modern Physics A
- 2019

The tilde conjugation rule in thermofield dynamics, equivalent to the modular conjugation in a [Formula: see text]-algebra, is used to develop unitary representations of the Poincaré group, where the… Expand

Phase Space Quantum Mechanics

- Physics, Mathematics
- 2010

The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an… Expand

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

- Mathematics, Physics
- 2006

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators… Expand

Wigner functions, contact interactions, and matching

- Physics
- 2007

Abstract Quantum mechanics in phase space (or deformation quantization) appears to fail as an autonomous quantum method when infinite potential walls are present. The stationary physical Wigner… Expand

The quantum state of the universe from deformation quantization and classical-quantum correlation

- Physics
- 2016

In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl–Wigner–Groenewold–Moyal formalism of phase space quantization, with perfect fluid as a matter source.… Expand

Semiquantum versus semiclassical mechanics for simple nonlinear systems (10 pages)

- Physics
- 2006

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space,… Expand

Nambu quantum mechanics: A Nonlinear generalization of geometric quantum mechanics

- Physics
- 2002

We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the… Expand

New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering

- Physics
- 2010

Using the Weyl ordering of operators expansion formula (Hong-Yi Fan, J. Phys. A 25 (1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator Δ (q',p')… Expand

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