Elimination of divergence for the problem of a particle in a scalar quantum field

  • Ilya D. Feranchuk Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Oleg D. Skoromnik Independent researcher, Heidelberg, Germany
  • Nguyen Quang San Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract

The problem of the interaction of a particle with a scalar quantum field is considered. The use of perturbation theory in this problem leads to ultraviolet divergence in the calculation of the ground state energy, for the renormalisation of which it is necessary to use an indefinite parameter – momentum cutoff. The work describes an iteration scheme for calculating the observed characteristics of the system, which allows to go beyond the perturbation theory. The dependence of the ground state energy on the coupling constant was found and it is shown that it does not contain divergence, but it has a logarithmic singularity in the limit, when the coupling constant of the particle with the field tends to zero. Such a function cannot be represented as a power series over the coupling constant, which explains the inapplicability of the standard perturbation theory. The result obtained is of fundamental importance for quantum field theory, since it shows that the momentum cutoff, which is used for renormalisation when calculating physical quantities, is determined by the parameters of the system, and the divergences are due to the presence of a singularity in the dependence of these quantities on the coupling constant.

Author Biographies

Ilya D. Feranchuk, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

doctor of science (physics and mathematics), full professor; professor at the department of theoretical physics and astrophysics, faculty of physics

Oleg D. Skoromnik, Independent researcher, Heidelberg, Germany

independent researcher

Nguyen Quang San, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics); researcher at the department of theoretical physics and astrophysics, faculty
of physics

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Published
2023-01-26
Keywords: regularisation, perturbation theory, ultraviolet divergence, quantum field theory, quantum electrodynamics, operator method
How to Cite
Feranchuk, I. D., Skoromnik, O. D., & San, N. Q. (2023). Elimination of divergence for the problem of a particle in a scalar quantum field. Journal of the Belarusian State University. Physics, 1, 4–13. https://doi.org/10.33581/2520-2243-2023-1-4–13