Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Peculiarities of the Weyl - Wigner - Moyal formalism for scalar charged particles

Bohdan I. Lev, А. А. Семенов, Constantin V. Usenko

Published Jan 1, 2001• 5 citations
OpenAlex

Abstract

Description of scalar charged particles, based on the Feshbach - Villars formalism, is proposed. Particles are described by an object that is Wigner function in usual coordinates and momentums and density matrix in charge variable. It is possible to introduce the usual Wigner function for a large class of dynamical variables. Such an approach contains explicitly a measuring device frame. From our point of view it corresponds to the Copenhagen interpretation of quantum mechanics. It is shown how physical properties of such particles depend on the definition of operator of coordinate. Evolution equation for the Wigner function of a single-charge state in classical limit coincides with the Liouville equation. Localization peculiarities manifest themselves in specific constraints on possible initial conditions.

Related papers

Peculiarities of the Weyl-Wigner-Moyal formalism for scalar charged particles

B I Lev, A A Semenov, C V Usenko

A description of scalar charged particles, based on the Feshbach-Villars formalism, is proposed. Particles are described by an object that is a Wigner function in usual coordinates and momenta and a density matrix in the charge variable. It is possible to introduce the usual Wigner function for a large class of dynamical variables. Such an approach explicitly contains a measuring device frame. From our point of view it corresponds to the Copenhagen interpretation of quantum mechanics. It is shown how physical properties of such particles depend on the definition of the coordinate operator. The evolution equation for the Wigner function of a single-charge state in the classical limit coincides with the Liouville equation. Localization peculiarities manifest themselves in specific constraints on possible initial conditions.

arXiv:quant-ph/0102095•Journal of Physics A Mathematical and General•May 9, 2001•4 citations

Phase space localization of a scalar charged particle

А. А. Семенов

The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The evolution equations are found to coincide with their counterparts in relativistic quantum mechanics with non-local Hamiltonian. The difference between the theories is connected with peculiarities of the constraints on the initial conditions. Effective increase in coherence between eigenstates of the Hamiltonian is found. Relativistic coherent states that take into account a non-trivial charge structure of the position and momentum operators and satisfy the charge superselection rule are considered. On this basis, the entangled coherent states are developed.

arXiv:quant-ph/0206050•Jun 7, 2002•0 citations

Possible peculiarities of synchrotron radiation in a strong magnetic field

Bohdan I. Lev, А. А. Семенов, Constantin V. Usenko

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. For observables independent of charge variable, we propose relativistic Wigner function formalism that contains explicitly the measurement device frame. This approach can provide the description of charged particles gas (plasma). It differs from the traditional one but is consistent with the Copenhagen interpretation of quantum mechanics. The effects that are connected with this approach can be observed in astrophysical objects - neutron stars.

arXiv:quant-ph/0011027•Nov 7, 2000•1 citation

Relativistic Wigner Function, Charge Variable and Structure of Position Operator

Bohdan I. Lev, А. А. Семенов, Constantin V. Usenko

The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed. The dynamical equation coincides with its analogue in the non-local theory (generalization of the Newton-Wigner position operator approach) under conditions when particles creation is impossible. Differences reveal themselves in specific constraints on possible initial conditions.

arXiv:quant-ph/0112122•Dec 20, 2001•0 citations

Gauge-invariant relativistic Wigner functions

Sndor Varr, Juha Javanainen

On the basis of the Hamiltonian form of the Klein–Gordon equation for a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2 × 2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and whose off-diagonal elements correspond to cross-densities in phase space. The system of coupled transport equations has been derived in the case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic and the classical limits of the relativistic quantum Boltzmann–Vlasov equation are discussed. In the nonrelativistic limit ( p / mc → 0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities. In the classical limit (ℏ → 0) two relativistic Boltzmann–Vlasov equations result for the diagonal positon and negaton densities. Even though the Planck constant ℏ is absent from the latter equations, the real part of the positon–negaton cross-density does not vanish.

Journal of Optics B Quantum and Semiclassical Optics•Jun 1, 2003•11 citations

The Weyl – Wigner – Moyal Formalism on a Discrete Phase Space. II. The Photon Wigner Function

Maciej Przanowski, Jaromir Tosiek, Francisco J. Turrubiates

Abstract Classical model of light in helicity formalism is presented. Then quantum mechanical point of view at photons – construction and interpretation of two equivalent photon wave functions are proposed. Quantum mechanics of photon is investigated. The Białynicki – Birula scalar product and the generalized Hermitian conjugation of linear operator are discussed. Quantum description of light on a phase space based on the Weyl – Wigner – Moyal approach is developed. A photon Wigner function is built. Some explicit photon Wigner functions for different kernels are obtained.

arXiv:2006.12833•Fortschritte der Physik•Oct 27, 2020•5 citations
Description of scalar charged particles, based on the Feshbach - Villars formalism, is proposed. Particles are described by an object that is Wigner function in usual coordinates and momentums and density matrix in charge variable. It is possible to introduce the usual Wigner function for a large class of dynamical variables. Such an approach contains explicitly a measuring device frame. From our point of view it corresponds to the Copenhagen interpretation of quantum mechanics. It is shown how physical properties of such particles depend on the definition of operator of coordinate. Evolution equation for the Wigner function of a single-charge state in classical limit coincides with the Liouville equation. Localization peculiarities manifest themselves in specific constraints on possible initial conditions.
A description of scalar charged particles, based on the Feshbach-Villars formalism, is proposed. Particles are described by an object that is a Wigner function in usual coordinates and momenta and a density matrix in the charge variable. It is possible to introduce the usual Wigner function for a large class of dynamical variables. Such an approach explicitly contains a measuring device frame. From our point of view it corresponds to the Copenhagen interpretation of quantum mechanics. It is shown how physical properties of such particles depend on the definition of the coordinate operator. The evolution equation for the Wigner function of a single-charge state in the classical limit coincides with the Liouville equation. Localization peculiarities manifest themselves in specific constraints on possible initial conditions.
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The evolution equations are found to coincide with their counterparts in relativistic quantum mechanics with non-local Hamiltonian. The difference between the theories is connected with peculiarities of the constraints on the initial conditions. Effective increase in coherence between eigenstates of the Hamiltonian is found. Relativistic coherent states that take into account a non-trivial charge structure of the position and momentum operators and satisfy the charge superselection rule are considered. On this basis, the entangled coherent states are developed.
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. For observables independent of charge variable, we propose relativistic Wigner function formalism that contains explicitly the measurement device frame. This approach can provide the description of charged particles gas (plasma). It differs from the traditional one but is consistent with the Copenhagen interpretation of quantum mechanics. The effects that are connected with this approach can be observed in astrophysical objects - neutron stars.
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed. The dynamical equation coincides with its analogue in the non-local theory (generalization of the Newton-Wigner position operator approach) under conditions when particles creation is impossible. Differences reveal themselves in specific constraints on possible initial conditions.
On the basis of the Hamiltonian form of the Klein–Gordon equation for a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2 × 2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and whose off-diagonal elements correspond to cross-densities in phase space. The system of coupled transport equations has been derived in the case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic and the classical limits of the relativistic quantum Boltzmann–Vlasov equation are discussed. In the nonrelativistic limit ( p / mc → 0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities. In the classical limit (ℏ → 0) two relativistic Boltzmann–Vlasov equations result for the diagonal positon and negaton densities. Even though the Planck constant ℏ is absent from the latter equations, the real part of the positon–negaton cross-density does not vanish.
Abstract Classical model of light in helicity formalism is presented. Then quantum mechanical point of view at photons – construction and interpretation of two equivalent photon wave functions are proposed. Quantum mechanics of photon is investigated. The Białynicki – Birula scalar product and the generalized Hermitian conjugation of linear operator are discussed. Quantum description of light on a phase space based on the Weyl – Wigner – Moyal approach is developed. A photon Wigner function is built. Some explicit photon Wigner functions for different kernels are obtained.