Related papers: Deformation Quantization: Quantum Mechanics Lives …
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution.…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
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. The corresponding quantum cosmology is…
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the…
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the…
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 appropriate deformation of the classical…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…
We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a $\star$-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner…
A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…
We show that the de Broglie-Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we…
The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion…
In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…
The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space.…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.