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The conventional Wigner function is inappropriate in a quantum field theory setting because, as a quasiprobability density over phase space, it is not manifestly Lorentz covariant. A manifestly relativistic variant is constructed as a…
We study the propagation of high-frequency electromagnetic waves in randomly heterogeneous bianisotropic media with dissipative properties. For that purpose we consider randomly fluctuating optical responses of such media with correlation…
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 analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and…
The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar…
We study degenerate three photon down conversion as a potential scheme for generating nonclassical states of light which exhibit clear signatures of phase space interference. The Wigner function representing these states contains an…
Synchrotron radiation emitted by electrons passing through an undulator placed in a storage ring is decomposed in coherent modes. The case of ultimate storage rings where the electron emittance is comparable to the emittance of the photon…
4-dimensional optics is here introduced axiomatically as the space that supports a Universal wave equation which is applied to the postulated Higgs field. Self-guiding of this field is shown to produce all the modes necessary to provide…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
The relation of the Wigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics…
The presence of negative values in the Wigner quasiprobability distribution is deemed one of the hallmarks of nonclassical phenomena in quantum systems. Here we demonstrate a classical model of squeezed light that, when combined with…
In this paper, we address the phase space formulation of the Jaynes-Cummings model through the explicit construction of the full Wigner function for a hybrid bipartite quantum system composed of a two-level atom and a quantized coherent…
Corresponding to optical Fresnel transformation characteristic of ray transfer matrix elements (A;B;C;D); AD-BC = 1, there exists Fresnel operator F(A;B;C;D) in quantum optics, we show that under the Fresnel transformation the pure position…
The generalized parton distributions, introduced nearly a decade ago, have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and…
The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability…
Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics.…
In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations…
Super- and subradiance are usually described in the framework of Dicke collective states, which is an ``atomic picture'' in which the electromagnetic field only provides an effective interaction between the atoms. Here, we discuss a…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
We calculate the Wigner (quasi)probability distribution function of the quantum optical elliptical vortex (QEV), generated by coupling squeezed vacuum states of two modes. The coupling between the two modes is performed by using beam…