https://doi.org/10.1140/epjp/s13360-023-03838-0
Regular Article
Redefinition of the energy–momentum operator: motivation and implications
1
Belarusian State University, Minsk, Belarus
2
Istanbul Okan University, Istanbul, Turkey
3
Institute for Nuclear Problems, Belarusian State University, Minsk, Belarus
Received:
16
January
2023
Accepted:
22
February
2023
Published online:
11
March
2023
The paper is motivated by our idea to re-define the momentum operator in quantum physics through the sum of mechanical and electromagnetic momenta for the system “charged particle in an electromagnetic field” instead of its canonical momentum, which occurred successful in describing quantum phase effects for charges and dipoles (Kholmetskii et al. in Ann. Phys. 392:49, 2018; Sci. Rep. 8:11,937, 2018). Furthermore, we show how a recently obtained expression for the “point-by-point” quantum phase of a charged particle in the framework of a fully quantized model of the Aharonov–Bohm effect (Marletto and Vedral in Phys. Rev. Lett. 125:040,401, 2020) supports the re-definition of the momentum operator in quantum mechanics from the theoretical side. These results motivated us to re-analyze the fundamental equations of relativistic quantum mechanics with a new energy–momentum operator. In this contribution, we solve the Dirac equation for an electrically bound electron with a new energy–momentum operator and extend the obtained solutions to the precise physics of simple atoms in the form of an effective theory, which does not touch the diagram technique of QED. We find that for majority of problems of precise physics of simple atoms, both definitions of the energy–momentum operator, yield indistinguishable results with modern measurement precision. An important exception is the spectroscopy of ortho-positronium, which occurs crucial in choosing the correct expression for the energy–momentum operator, and it shows that the available measurement data rather support the new definition of this operator.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
