https://doi.org/10.1140/epjp/s13360-023-04463-7
Regular Article
Scattering approach for calculating one-loop effective action and vacuum energy
1
Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, 300071, Tianjin, People’s Republic of China
2
College of Physical Science and Technology, Bohai University, 121013, Jinzhou, People’s Republic of China
3
College of Physics and Materials Science, Tianjin Normal University, 300387, Tianjin, People’s Republic of China
4
Department of Physics, Tianjin University, 300350, Tianjin, People’s Republic of China
Received:
3
May
2023
Accepted:
10
September
2023
Published online:
25
September
2023
We propose an approach for calculating one-loop effective actions and vacuum energies in quantum field theory. Spectral functions are functions defined by the eigenvalues of an operator. One-loop effective actions and vacuum energies in quantum field theory, as well as scattering phase shifts and scattering amplitudes in quantum mechanics, are all spectral functions. If a transformation between different spectral functions is identified, we can obtain a spectral function from another through the transformation. In this paper, we convert quantum mechanical methods for calculating scattering phase shifts and scattering amplitudes into quantum field theory methods for calculating one-loop effective actions and vacuum energies.
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© 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.
