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arXiv:2208.01742

Quantum fluctuations, quanta of electromagnetic interaction, quantum electronic bound states

V. N. Murzin, Ljudmila Yu. Shchurova

Published Jul 31, 2022• 0 citations
arXivHTMLPDF

Abstract

Based on the concepts of the quantum field theory of virtual photons as quanta of electromagnetic interaction, we discuss the physical content of the phenomena underlying the principle of quantum uncertainties. We consider the features of the uncertainty relations and the properties of the elementary particles (electrons, protons, etc.) under the conditions of the formation of quantum bound states at atomic and subatomic distances.

DOI
10.48550/arxiv.2208.01742

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Based on the concepts of the quantum field theory of virtual photons as quanta of electromagnetic interaction, we discuss the physical content of the phenomena underlying the principle of quantum uncertainties. We consider the features of the uncertainty relations and the properties of the elementary particles (electrons, protons, etc.) under the conditions of the formation of quantum bound states at atomic and subatomic distances.
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Abstract This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.
The wave-structure of moving electrons is analyzed on a fundamental level by employing a modified de Broglie relation. Formalizing the wave-function ψψψ in real notation yields internal energy components due to mass oscillations. The wave-features can then be referred to physical waves of discrete frequency ννν and the classical dispersion relation $λν= u $, complying with the classical wave equation. Including external potentials yields the Schrödinger equation, which, in this context, is arbitrary due to the internal energy components. It can be established that the uncertainty relations are an expression of this, fundamental, arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. The wave equations of intrinsic particle properties are Lorentz invariant considering total energy of particles, although transformations into a moving reference frame lead to an increase of intrinsic potentials. Interactions of photons and electrons are treated extensively, the results achieved are equivalent to the results in quantum theory. Electrostatic interactions provide, a posteriori, a justification for the initial assumption of electron-wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. The concept finally allows the conclusion that a significant correlation for a pair of spin particles in EPR--like measurements is likely to violate the uncertainty relations.