Related papers: Schwinger, Pegg and Barnett approaches and a relat…
Gauge freedom in quantum particle physics is shown to arise in a natural way from the geometry of two-spinors (Weyl spinors). Various related mathematical notions are reviewed, and a special ansatz of the kind "the system defines the…
Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete…
We prove that Wigner functions contain a symplectic connection. The latter covariantises the symplectic exterior derivative on phase space. We analyse the role played by this connection and introduce the notion of local symplectic…
Generalized Weyl quantization formalism for the cylindrical phase space $S^1 \times \mathbb{R}^1$ is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be…
The physical phase space of gauge field theories on a cylindrical spacetime with an arbitrary compact simple gauge group is shown to be the quotient $ {\bf R}^{2r}/W_A, $ $ r $ a rank of the gauge group, $ W_A $ the affine Weyl group. The…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy…
It is well known that the expansion of the universe can create particles. However, due to ambiguities when defining particles during the expansion, there are still debates about how to choose vacuum and particle states. To clarify how…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
An adaptation of the WKB method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between…
Coherent states possess a regularized path integral and gives a natural relation between classical variables and quantum operators. Recent work by Klauder and Whiting has included extended variables, that can be thought of as gauge fields,…
A new definition of the Wigner function for quantum fields coupled to curved space--time and an external Yang--Mills field is studied on the example of a scalar and a Dirac fields. The definition uses the formalism of the tangent bundles…
The recently proposed scheme for direct sampling of the quantum phase space by photon counting is discussed within the Wigner function formalism.
Introduction Phase space methods in quantum mechanics - The Wigner function - The Husimi function - Inverse participation ratio Anderson model in phase space - Husimi functions - Inverse participation ratios
We show that classicality emerges during quantum phase transitions due to parametric interactions without coupling to environments. The Wigner functions are explicitly calculated for the Gaussian vacuum, number, and thermal states of a free…
An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a…
Entanglement of bipartite squeezed states generated by holomorphic Hermite functions of two complex variables is investigated using phase-space approach based on the Wigner distribution function. Orthogonality of the holomorphic Hermite…
A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…
The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…