Quantum states of an electromagnetic field interacting with a classical current and their applications to radiation problems

Abstract

<jats:p>Synchrotron radiation was originally studied by classical methods using the Liénard–Wiechert potentials of electric currents. Subsequently, quantum corrections to the classical formulas were studied, considering the emission of photons arising from electronic transitions between spectral levels, described in terms of the Dirac equation. In this paper, an intermediate approach is considered, in which electric currents generating the radiation are considered classically while the quantum nature of the radiation is taken into account exactly. Such an approximate approach may be helpful in some cases; it allows one to study one-photon and multi-photon radiation without complicating calculations using corresponding solutions of the Dirac equation. Here, exact quantum states of an electromagnetic field interacting with classical currents are constructed and their properties studied. With their help, the probability of photon emission by classical currents is calculated and relatively simple formulas for one-photon and multi-photon radiation are obtained. Using the specific circular electric current, the corresponding synchrotron radiation is calculated. The relationship between the obtained results and those known before are discussed, for example with the Schott formula, with Schwinger calculations, with one-photon radiation of scalar particles due to transitions between Landau levels, and with some previous results of calculating two-photon synchrotron radiation.</jats:p>

Electromagnetic radiation of accelerated charged particle in the framework of a semiclassical approach

“…In contrast to the energy (30), the rate (35) is asymmetrical with respect to time because the time derivative in (29) affects only the upper integration limit of function y kλ (t, t in ). As a result, the energy rates computed from (29) or (35) shall feature the same type of asymmetry. However, it is possible to define a symmetrical energy rate choosing t = T /2 = −t in and differentiating the corresponding energy with respect to T : w (T ) ≡ ∂ ∂T W (+T /2, −T /2).…”

“…In the work [29], it was proposed the so-called semiclassical approach for describing quantum properties of radiation of currents of charged particles. In this approach, currents, generating the radiation are considered classically, whereas the quantum nature of the radiation is taken into account exactly.…”

“…However, an univocal correspondence between every charge trajectory and a corresponding electromagnetic field does not exist. The efficacy of the semiclassical approach was demonstrated in calculating synchrotron [29] and undulator [30] radiations. In the present article we apply the semiclassical approach to study electromagnetic radiation by uniformly accelerated charged particles.…”

“…2 we present the basic formulation of the semiclassical description of electromagnetic radiation in the general case, refining and supplementing the results presented in the original Refs. [29,30]. In Sect.…”

Electromagnetic Radiation of Accelerated Charged Particle in the Framework of a Semiclassical Approach

“…In Section 2 we present the basic formulation of the semiclassical description of electromagnetic radiation in the general case, refining and supplementing the results presented in the original refs. [33,34]. In Section 3, we apply these results to calculate electromagnetic energies and rates radiated by an accelerated charge.…”