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Journal of Physics Conference Series

On the issue of quantum theory of the Fresnel reflection

B. A. Veklenko

Published Nov 1, 2019• 1 citation
Publisher

Abstract

Abstract A new method for solution of the quantum electrodynamics equations is proposed. This method makes it possible to avoid the procedure of breaking the quantum correlators and bridges the gap between the theories of Maxwell gases and the theories of superconductivity and superfluidity. As an example, the quantum theory of the Fresnel reflection is considered. It is shown that, even outside the scattering layer, there are the photon states correlated with the scattering layer by means of the quantum correlations. In particular, such photons form two reflected beams previously unknown.

DOI
10.1088/1742-6596/1383/1/012030

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Abstract A new method for solution of the quantum electrodynamics equations is proposed. This method makes it possible to avoid the procedure of breaking the quantum correlators and bridges the gap between the theories of Maxwell gases and the theories of superconductivity and superfluidity. As an example, the quantum theory of the Fresnel reflection is considered. It is shown that, even outside the scattering layer, there are the photon states correlated with the scattering layer by means of the quantum correlations. In particular, such photons form two reflected beams previously unknown.
Electromagnetic phenomena can be either classically described with the help of Maxwell's equations, or by the methods of quantum computing and Schrodinger equation. In the present paper we will describe the phenomena of reflection and refraction using only quantum mechanical methods. Finally, we get Fresnel's equations without to call on the classical electromagnetic equations. The method involves the use of wave functions of the photon in the momentum representation, compiled with a polarization term, and keeps the promise of a simple way of calculating the behavior of photonic devices as used in optoelectronics.
According to quantum electrodynamics, the cross section for resonant scattering of radiation on an aggregate of excited atoms can be written as a sum of positive definite terms. This type of structure is not consistent with the Fresnel formulas for the reflection coefficient of radiation from thermally excited media. The difference shows up on a macroscopic level and indicates that semiclassical radiation theory cannot be used. A study of the correlation between elastic scattering and stimulated emission processes clarifies the reason for the discrepancies. The resulting singularities require summing of Feynman diagrams which appear beginning in the sixth order of perturbation theory. A lower bound estimate for the reflection coefficient from a plane layer is given, including processes which violate the statistics of radiation. The contribution of stimulated emission processes caused by the initially scattered photon are examined specifically. An experiment is proposed which would settle the choice of theories.
Abstract Three linear equations are proposed as quantum-mechanical equations for the free propagating photons. The solution of these equations is the vector potential of the electromagnetic field and it is a product of the Gaussian functions for the transverse coordinates and the eigenfunction of the harmonic oscillator for the longitudinal coordinate. This solutions is used to describe the reflection and refraction of photons on the boundary between two dielectrics. The amplitude of the reflected field coincides with the Fresnel formulae for the plane waves, but the amplitude of the refracted field is different. These amplitudes are the probability’s amplitudes of reflection and refraction of photons—like in the quantum mechanics. The photons propagated from the first into the second medium increase (decrease) their transverse size in the plane of incidence, if the refraction index of the second medium is greater (smaller) than in the first medium. The increasing or decreasing grow when increasing the angle of incidence. The difference between the quantum mechanics of the particles with a mass and the photons, as well as the interpretation of the wave function of photons, is discussed.
It is demonstrated that presence of stimulated radiation processes in gaseous media makes it possible to generate rays inversely reflected from interfaces of thermally excited gaseous media and the processes of left-hand refraction of the rays having passed through these media. These processes are caused by availability of coupled photonic states and stimulated radiation in media the properties of which differ from those of stimulated radiation in vacuum. Estimation of these processes is based on exclusion of the procedure of forced breaking of quantum correlators and correct consideration of high-order correlators. Along with Schrödinger’s and Heisenberg’s representations, this article uses also the less-known Γ- representation, which allows us to reduce a multi-particle problem of quantum electrodynamics to a single-particle problem within the an infinite-dimensional space. The equations formed in Г- representation are mathematically simpler and may be studied using the standard Wick’s theorem rather than its approximated thermodynamic variant suggested by T.A. Matsubara. Therefore it is possible to keep all possible solutions of the initial system of equations in mind. Of course, approximation methods are used for explicit solution of these equations. Using Feynman diagrams instead of the Dyson equation for quantum correlators, it is possible to find an equation defining the complete density matrix of a photonic sub-system.
Due to the advent of Quantum Mechanics' 100th anniversary in 2025, we wrote this review paper in order to present a discussion that addresses the foundations of this theory. And since the creation of this Mechanics and other quantum theories was guided, for instance, by correspondence principles that needed to be identified between them and other well-established physical theories, this paper will be devoted to discussing the correspondence between these quantum theories and Maxwell's theory of electromagnetism. More precisely, what we will do throughout this paper is discuss how the Maxwell's electromagnetic theory in free space and the stronger formulation of the correspondence principle already pointed, together, to the basis of a Quantum Mechanics that was only be formulated half a century later. And, in order to make this very clear, we will show that the quantum-mechanical description of a photon can already be identified, simply, by manipulating Maxwell's equations in free space with mathematical resources that, for instance, were already well known before the advent of Quantum Mechanics.