Related papers: A relativistic variant of the Wigner function
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…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states -- called Wigner entropy for…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the…
The evolution of the discrete Wigner function is formally similar to a probabilistic process, but the transition probabilities, like the discrete Wigner function itself, can be negative. We investigate these transition probabilities, as…
A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…
We show how sub-Planck phase-space structures in the Wigner function can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent…
Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides…
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation…
In this essay we review the central difficulty in formulating a viable quantum field theory in which gravity is emergent at low energies, rather than mediated by a fundamental gauge field. The Weinberg-Witten theorem forbids spin 2 massless…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
Exploring the concept of the extended Galilei group $\mathcal{G}$, a representation for the symplectic quantum mechanics in the manifold of $\mathcal{G}$, written in the light-cone of a five-dimensional De Sitter space-time, is derived…
I present a relativistic covariant version of the Bohmian interpretation of quantum mechanics and discuss the corresponding measurable predictions. The covariance is incoded in the fact that the nonlocal quantum potential transforms as a…
I describe a method of inferring the past of quantum observables given the initial state and the subsequent measurement results using Wigner quasi-probability representations. The method is proved to be compatible with logic for large…
We review the method for constructing local relativistic fields corresponding to the Bargmann-Wigner wave functions that describe the unitary irreducible representations of the $4D$ Poincar\'{e} group. The method is based on the use of the…
We give a simple and direct construction of a massless quantum field with arbitrary discrete helicity that satisfies Wightman axioms and the corresponding relativistic wave equation in the distributional sense. We underline the mathematical…
In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here…
The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hbar\to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the…
The quantum electromagnetic (EM) field is formulated in the Weyl-Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle it is possible to interpret within WW all experiments involving the EM…