https://doi.org/10.1140/epjp/s13360-024-04929-2
Regular Article
Does a massless Goldstone boson exist?
National Science Center “Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
a yuripoluektov@kipt.kharkov.ua, y.poluekt52@gmail.com
Received:
4
May
2023
Accepted:
22
January
2024
Published online:
4
February
2024
Classical and quantum complex nonlinear scalar fields are considered. A new approach to the quantization of nonlinear fields and the construction of a perturbation theory with allowance for spontaneous symmetry breaking is proposed, based on the use of the relativistic model of a self-consistent field as the main approximation. The concept of a particle is analyzed within the framework of the theory of nonlinear quantum fields. When constructing single-particle states, the contribution of vacuum fluctuations is systematically taken into account. Within the framework of the developed approach, the problem of the existence of massless scalar particles is discussed. It is shown that successive consideration of the vacuum averages of not only one field operator, but also the products of two field operators, leads to the appearance of masses for scalar particles. Various states in which the field can exist for given parameters entering into the Lagrangian are considered, and the vacuum energy densities in these states are calculated. It is shown that, depending on the values of the parameters entering into the Lagrangian, the vacuum energy density can be either positive or negative, which is important for modern cosmology.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.