Quantum electrodynamics of one scalar particle

The theory of the interaction between a complex scalar field and the electromagnetic field is presented with initial and final conditions that allow an interpretation in the context of the relativistic quantum mechanics of a single charged scalar particle. Included are particle scattering, antiparticle scattering, pair creation, and pair annihilation due to a classical dynamical electromagnetic field. The equations of motion are solved by a perturbation expansion, which does not lead to the troublesome divergent terms of quantum field theory.     

Quantum electron self-interaction in a strong laser field

The quantum state of an electron in a strong laser field is altered if the interaction of the electron with its own electromagnetic field is taken into account. Starting from the Schwinger-Dirac equation, we determine the states of an electron in a plane-wave field with inclusion, at leading order, of its electromagnetic self-interaction. On the one hand, the electron states show a pure quantum contribution to the electron quasimomentum, conceptually different from the conventional classical one arising from the quiver motion of the electron. On the other hand, the electron self-interaction induces a distinct dynamics of the electron spin, whose effects are shown to be measurable in principle with available technology.     

The classical field limit of scattering theory for non-relativistic many-boson systems. I

We study the classical field limit of non-relativistic many-boson theories in space dimensionn≧3. When ?→0, the correlation functions, which are the averages of products of bounded functions of field operators at different times taken in suitable states, converge to the corresponding functions of the appropriate solutions of the classical field equation, and the quantum fluctuations are described by the equation obtained by linearizing the field equation around the classical solution. These properties were proved by Hepp [6] for suitably regular potentials and in finite time intervals. Using a general theory of existence of global solutions and a general scattering theory for the classical equation, we extend these results in two directions: (1) we consider more singular potentials, (2) more important, we prove that for dispersive classical solutions, the ?→0 limit is uniform in time in an appropriate representation of the field operators. As a consequence we obtain the convergence of suitable matrix elements of the wave operators and, if asymptotic completeness holds, of theS-matrix.     

Radiation reaction

I solve Maxwell's equation for a current produced by a classical, point electron. My solution, which represents the self electromagnetic field of the electron, can be found along the electron trajectory, where the conventional retarded-time solution is singular. The solution is in the form of an integral over all spectral frequencies of the field and has an Ehrenfest correspondence with the operator field of quantum electrodynamics (QED). Use of the field in the equation of motion for a harmonically-bound electron leads to an equation having the same form as the Schrödinger equation for a two-level atom interacting with the QED vacuum field.     

Resonant absorption of electromagnetic radiation in a quantum channel due to the scattering of electrons by impurities

We have found an analytical expression for the absorption coefficient of electromagnetic radiation in a quantum channel with a parabolic confinement potential. The calculation has been performed using the second-order perturbation theory taking into account the scattering of a quasi-one-dimensional electron gas by ionized impurities. We have analyzed the dependences of the absorption coefficient on the frequency of the electromagnetic radiation and the magnetic field. The appearance of additional resonant peaks, which are caused by scattering by impurities, has been found.     

Quantum theory of self-induced transparency

It is known that classical electromagnetic radiation at a frequency in resonance with energy splittings of atoms in a dielectric medium can be described using the classical sine-Gordon theory. In this paper we quantize the electromagnetic field and compute some quantum effects by using known results from the sine-Gordon quantum field theory. In particular, we compute the intensity of spontaneously emitted radiation using the thermodynamic Bethe ansatz with boundary interactions.     

Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.     

Space-time trajectories of quantum particles

The concept of trajectory is extended theoretically from classical mechanics through nonrelativistic and relativistic quantum mechanics. Forced motion of the particle as might be caused by an electromagnetic field is included in the equations. A new interpretation of the electromagnetic potential and the gauge transformation is presented. Using this formal structure, the problem of collecting particles into packets using trajectories is studied for both quantum mechanics and classical mechanics. Quantum mechanical trajectories are found to be significantly more restricted than those allowed by classical physics. The uncertainty principle comes from the second-order nature of the field equation without recourse to statistical arguments. The trajectories of particles in a quantum state can be calculated explicitly from the wave function (also see article in Volume 20, Number 6).     

Proof of the Evans-Vigier field from the dirac equation of the fermion in the classical field: Reply to Rikken

The Dirac equation of the fermion in the classical electromagnetic field is used to prove the existence of the Evans-Vigier field from the first principles of relativistic quantum theory.     

The electron in the quantum field of a plane wave and the classical field of Redmond configuration

The Dirac equation is solved exactly for an electron interacting with both the quantum field of a plane wave and with a classical electromagnetic field, consisting of a plane wave and a constant, homogeneous magnetic field, parallel to the direction of propagation of both waves.     

The classical field limit of scattering theory for non-relativistic many-boson systems. II

We study the classical field limit of non relativistic many-boson theories in space dimensionn3, extending the results of a previous paper to more singular interactions. We prove the expected results: when tends to zero, the quantum theory tends in a suitable sense to the corresponding classical field theory, and the quantum fluctuations are governed by the equation obtained by linearizing the quantum evolution equation around the classical solution. These results hold uniformly in time and therefore apply to scattering theory. The interactions considered here are so singular as to require a change of domain in order to define the generator of the evolution of the fluctuations, but sufficiently regular so that no energy renormalization is needed.     

Quantum kinetic theory of trapped particles in a strong electromagnetic field

The idea of treating quantum systems by semiclassical representations using effective quantum potentials (forces) has been successfully applied in equilibrium by many authors, see e.g. [D. Bohm, Phys. Rev. 85 (1986) 166 and 180; D.K. Ferry, J.R. Zhou, Phys. Rev. B 48 (1993) 7944; A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A 36 (2003) 5957 and references cited therein]. Here, this idea is extended to nonequilibrium quantum systems in an external field. A gauge-invariant quantum kinetic theory for weakly inhomogeneous charged particle systems in a strong electromagnetic field is developed within the framework of nonequilibrium Green’s functions. The equation for the spectral density is simplified by introducing a classical (local) form for the kinetics. Nonlocal quantum effects are accounted for in this way by replacing the bare external confinement potential with an effective quantum potential. The equation for this effective potential is identified and solved for weak inhomogeneity in the collisionless limit. The resulting nonequilibrium spectral function is used to determine the density of states and the modification of the Born collision operator in the kinetic equation for the Wigner function due to quantum confinement effects.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example.     

Investigation of the particle spin properties on the velocity space instability in high‐density plasmas

The nonresonant electromagnetic instabilities of the anisotropic velocity space (Weibel‐like) have always been one of the interesting subjects for researchers. These electromagnetic instabilities play an important role in generating strong magnetic fields in laboratory plasmas for applications such as inertial confinement fusion and space plasmas. In this paper, we investigate the quantum effects of the particle spin on the electromagnetic instabilities. In the case of the presence of a magnetic dipole force and an electron precession frequency like the Vlasov equation, we derive the full quantum equation. This study shows that, in the presence of the spin‐polarized effects, the growth rate of the instabilities is reduced compared to the classical cases and will not arise for low fractions of the temperature anisotropy for different values of the magnetic field. Indeed, it is expected that the probability of electron capture in the background magnetic fields and the effective collision with the particle increase because of the spin effect, so that a high portion of the electron energy is transmitted to the background plasma, and the temperature anisotropy governing the electron distribution is reduced.     

Fermions without spinors

The classical Kähler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of the field contain only integer representations of the Lorentz group for a physical interpretation of the quantum theory, we impose fermionic commutators. The electromagnetic interactions are identical to those of a Dirac spinor field with an extra fourfold degeneracy. Possibilities for the interpretation of the extra degrees of freedom are discussed.     

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

The problem of the electromagnetic radiation produced by charge distributions in the framework of a semiclassical approach proposed in the work by Bagrov, Gitman, Shishmarev, and Farias Jr. [J. Synchrotron Rad. 27 , 902–911 (2020)] is addressed here. In this approach, currents, generating the radiation are considered classically, while the quantum nature of the radiation is kept exactly. Quantum states of the electromagnetic field are solutions of Schrödinger's equation, and relevant quantities to the problem are evaluated with the aid of transition probabilities. This construction allows us to introduce the quantum transition time in physical quantities and assess its role in radiation problems by classical currents. Radiated electromagnetic energies are studied in detail and a definition for the rate at which radiation is emitted from sources is presented. In calculating the total energy and rate radiated by a pointlike charged particle accelerated by a constant and uniform electric field, it is discovered that these results are compatible with results obtained by other authors in the framework of the classical radiation theory under an appropriate limit. Numerical and asymptotic analyses of the results are also performed.