About non-relativistic quantum mechanics and electromagnetism
- URL: http://arxiv.org/abs/2207.14390v1
- Date: Wed, 27 Jul 2022 05:05:27 GMT
- Title: About non-relativistic quantum mechanics and electromagnetism
- Authors: Ladislaus Alexander B\'anyai and Mircea Bundaru
- Abstract summary: We use the mathematical frame of the field theory and its quantization in the spirit of the quantum-mechanical many-body theory.
We show some examples of the importance of this extension of the many-body theory.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We describe here the coherent formulation of electromagnetism in the
non-relativistic quantum-mechanical many-body theory of interacting charged
particles. We use the mathematical frame of the field theory and its
quantization in the spirit of the QED. This is necessary because a manifold of
misinterpretations emerged especially regarding the magnetic field and gauge
invariance. The situation was determined by the historical development of
quantum mechanics, starting from the Schr\"odinger 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. Our approach to the non-relativistic QED emphasizes the role of
the gauge-invariance and of the external fields. We develop further the $1/c^2$
approximation of this theory allowing a closed description of the interacting
charged particles without photons. The resulting Hamiltonian coincides with the
quantized version of the Darwin Hamiltonian containing besides the Coulomb also
a current-current diamagnetic interaction. We show on some examples the
importance of this extension of the many-body theory.
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