Preprint Article Version 1 This version is not peer-reviewed

Quantum Mechanics and Electromagnetism. Non-Relativistic Theory.

Version 1 : Received: 4 May 2020 / Approved: 5 May 2020 / Online: 5 May 2020 (15:14:06 CEST)

How to cite: Banyai, L.A.; Bundaru, M. Quantum Mechanics and Electromagnetism. Non-Relativistic Theory.. Preprints 2020, 2020050083 (doi: 10.20944/preprints202005.0083.v1). Banyai, L.A.; Bundaru, M. Quantum Mechanics and Electromagnetism. Non-Relativistic Theory.. Preprints 2020, 2020050083 (doi: 10.20944/preprints202005.0083.v1).

Abstract

We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.

Subject Areas

nonrelativistic QED; many-body theories; Lagrangian; gauge invariance; Coulomb gauge; Hamiltonian; external fields; quantization; 1/c2 approximation; current-current interaction

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