Classical instanton solutions in quantum field theory

Authors

  • Roman G. Shulyakovsky Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus; Institute for Nuclear Problems, Belarusian State University, 11 Babrujskaja Street, Minsk 220006, Belarus
  • Alexander S. Gribowsky Joint Institute for Nuclear Research, 6 Joliot-Curie Street, Dubna 141980, Russia
  • Alexander S. Garkun Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus
  • Maxim N. Nevmerzhitsky Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus https://orcid.org/0000-0001-5621-2019
  • Alexei O. Shaplov Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus
  • Denis A. Shohonov Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus

Keywords:

instanton, quantum theory, quantum mechanics, gauge field, scalar field, confinement

Abstract

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

Author Biographies

  • Roman G. Shulyakovsky, Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus; Institute for Nuclear Problems, Belarusian State University, 11 Babrujskaja Street, Minsk 220006, Belarus

    PhD (physics and mathematics); leading researcher

  • Alexander S. Gribowsky, Joint Institute for Nuclear Research, 6 Joliot-Curie Street, Dubna 141980, Russia

    junior researcher

  • Alexander S. Garkun, Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus

    PhD (physics and mathematics); deputy director for research and innovation and leading researcher

  • Maxim N. Nevmerzhitsky, Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus

    researcher

  • Alexei O. Shaplov, Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus

    researcher

  • Denis A. Shohonov, Institute of Applied Physics, National Academy of Sciences of Belarus, 16 Akademičnaja Street, Minsk 220072, Belarus

    junior researcher

References

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Published

2020-06-07

Issue

No. 2 (2020): Journal of the Belarusian State University. Physics

Section

Physics of Electromagnetic Phenomena

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How to Cite

(1)
Shulyakovsky, R. G. .; Gribowsky, A. S. .; Garkun, A. S. .; Nevmerzhitsky, M. N.; Shaplov, A. O. .; Shohonov, D. A. . Classical Instanton Solutions in Quantum Field Theory. Журнал Белорусского государственного университета. Физика 2020, No. 2, 78-85. https://doi.org/10.33581/2520-2243-2020-2-78-85.
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