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

International Journal of Modern Physics B

THEORY OF SPONTANEOUS RADIATION BY BOSONS IN QUASI-CLASSICAL TRAJECTORY-COHERENT APPROXIMATION

Владимир Владимирович Белов, D Boltovskij, Andrey Yu. Trifonov

Published Aug 15, 1994• 11 citations
Publisher

Abstract

The first order quantum correction is obtained for the characteristics of spontaneous radiation as a functional of a classical trajectory by means of quasi-classical trajectory–coherent states method for relativistic spinless particle in an arbitrary external electro-magnetic field. It is shown that the power of boson radiation coincides up to O (ħ2), ħ → 0 with the power of electron radiation averaged over spin states calculated by the TC-states of the Dirac equation. Certain specific examples are considered on the base of a general formula for the radiation power in the non-relativistic approximation, in particular, an expression for the radiation power in an axially symmetric magnetic field is obtained.

DOI
10.1142/s0217979294001007

Related papers

Quasi-Classical Theory of a Relativistic Spinning Electron

Ralph Schiller

The quasi-classical spin theory is a modified Hamilton-Jacobi theory for a classical relativistic dipole whose space-time trajectory is coupled to its spin motion. The equations of this quasi-classical theory are almost identical with the second-order (squared) Dirac equation, and, in fact, form a new WKB approximation to the second-order Dirac equation. We quantize this theory by requiring that a classical spinor "wave function" be continuous and single valued, and that it satisfy an eigenvalue equation. We find for a particle in a uniform magnetic field, and in a Coulomb field, that this quasi-classical theory predicts the same energy and angular momentum eigenvalues as the Dirac theory. The quasi-classical theory is invariant under Lorentz transformation, spin rotations, and charge conjugation. The spinor wave functions are form invariant with respect to arbitrary canonical transformations.

Physical Review•Nov 1, 1962•21 citations

The quasiclassical approximation to Dirac equation. I

Kenji Yajima

The mathematical foundation to the quasi-classical approximation to the Dirac equation is discussed. After constructing the propagator $U^\kappa(t,s)$ and the quasi-classical propagator for the Dirac equation in an external electro-magnetic field, the usual quasi-classical approximation to the wave function $U^\kappa(t,s)(\exp (iS(x)/h)f)$ is obtained with error estimates in the Hilbert $L^2(R^3,C^4)$.

Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics•Mar 31, 1982•6 citations

QUASICLASSICAL TRAJECTORY-COHERENT STATES OF A NONRELATIVISTIC PARTICL)~ IN AN ARBITRARY ELECTROMAGNETIC FIELD

L.D. LANDAU

It is shown that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the SchrSdinger equation such that the mean quantum-mechanic al coordinates and momenta of these states are enact general solutions of the classical Hamilton equations. Such states are called trajectory-coher ent states. The wave functions of trajectory-coher ent states are obtained by Maslov's complex germ method. The simplest properties of these states are studied.

•Jan 1, 1982•0 citations

CONTRIBUTION TO THE THEORY OF COHERENT SPONTANEOUS RADIATION

V. M. Faǐn

Some problems relating to the theory of coherent spontaneous radiation are considered. It is shown that the interactton of the particles via the common radiation field leads to a shift in the proper frequencies of the system. (auth)

Zhur. Eksptl'. i Teoret. Fiz.•Mar 1, 1959•0 citations

Quasiclassical trajectory-coherent states of a particle in an arbitrary electromagnetic field

Vladislav G. Bagrov, Владимир Владимирович Белов, I. M. Ternov

In this paper we show that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the Schrödinger equation, such that the quantum-mechanical averages of the coordinates and the momenta with respect to these states are general exact solutions of the classical Hamiltonian equations. Such states are called trajectory-coherent states. The wave functions of the trajectory-coherent states are obtained by the complex germ method by V. P. Maslov. The simplest properties of these states are studied.

Journal of Mathematical Physics•Dec 1, 1983•48 citations

The complex WKB-Maslov method for the Dirac equation in a torsion field: I. Construction of trajectory-coherent states and the equation for spin

Vladislav G. Bagrov, Владимир Владимирович Белов, Andrey Yu. Trifonov +1 more

The investigation of the Dirac equation by the WKB-Maslov method (complex sprout method) in Minkowski-Cartan space with an arbitrary external electromagnetic field is carried out. The Ehrenfest-type complete set of quasi-classical trajectory-coherent states (TCS) for the Dirac equation up to the order of O(h(cross) 3 2/) at to 0 is constructed. These states have the form of wavepackets moving along the worldline of the charged particle. From the Dirac equation a classical relativistic spin equation is derived by the use of the TCS which coincides with the generalization of the well known Bargmann-Michel-Telegdi equation in the case of an arbitrary external torsion field.

Classical and Quantum Gravity•Jul 1, 1991•10 citations
The first order quantum correction is obtained for the characteristics of spontaneous radiation as a functional of a classical trajectory by means of quasi-classical trajectory–coherent states method for relativistic spinless particle in an arbitrary external electro-magnetic field. It is shown that the power of boson radiation coincides up to O (ħ2), ħ → 0 with the power of electron radiation averaged over spin states calculated by the TC-states of the Dirac equation. Certain specific examples are considered on the base of a general formula for the radiation power in the non-relativistic approximation, in particular, an expression for the radiation power in an axially symmetric magnetic field is obtained.
The quasi-classical spin theory is a modified Hamilton-Jacobi theory for a classical relativistic dipole whose space-time trajectory is coupled to its spin motion. The equations of this quasi-classical theory are almost identical with the second-order (squared) Dirac equation, and, in fact, form a new WKB approximation to the second-order Dirac equation. We quantize this theory by requiring that a classical spinor "wave function" be continuous and single valued, and that it satisfy an eigenvalue equation. We find for a particle in a uniform magnetic field, and in a Coulomb field, that this quasi-classical theory predicts the same energy and angular momentum eigenvalues as the Dirac theory. The quasi-classical theory is invariant under Lorentz transformation, spin rotations, and charge conjugation. The spinor wave functions are form invariant with respect to arbitrary canonical transformations.
The mathematical foundation to the quasi-classical approximation to the Dirac equation is discussed. After constructing the propagator Uκ(t,s)U^\kappa(t,s)Uκ(t,s) and the quasi-classical propagator for the Dirac equation in an external electro-magnetic field, the usual quasi-classical approximation to the wave function Uκ(t,s)(exp⁡(iS(x)/h)f)U^\kappa(t,s)(\exp (iS(x)/h)f)Uκ(t,s)(exp(iS(x)/h)f) is obtained with error estimates in the Hilbert L2(R3,C4)L^2(R^3,C^4)L2(R3,C4).
It is shown that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the SchrSdinger equation such that the mean quantum-mechanic al coordinates and momenta of these states are enact general solutions of the classical Hamilton equations. Such states are called trajectory-coher ent states. The wave functions of trajectory-coher ent states are obtained by Maslov's complex germ method. The simplest properties of these states are studied.
In this paper we show that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the Schrödinger equation, such that the quantum-mechanical averages of the coordinates and the momenta with respect to these states are general exact solutions of the classical Hamiltonian equations. Such states are called trajectory-coherent states. The wave functions of the trajectory-coherent states are obtained by the complex germ method by V. P. Maslov. The simplest properties of these states are studied.
The investigation of the Dirac equation by the WKB-Maslov method (complex sprout method) in Minkowski-Cartan space with an arbitrary external electromagnetic field is carried out. The Ehrenfest-type complete set of quasi-classical trajectory-coherent states (TCS) for the Dirac equation up to the order of O(h(cross) 3 2/) at to 0 is constructed. These states have the form of wavepackets moving along the worldline of the charged particle. From the Dirac equation a classical relativistic spin equation is derived by the use of the TCS which coincides with the generalization of the well known Bargmann-Michel-Telegdi equation in the case of an arbitrary external torsion field.