Approximate evaluation of the functional integrals generated by the Dirac equation with pseudospin symmetry
https://doi.org/10.29235/1561-2430-2021-57-1-14-22
Abstract
In this paper, the matrix-valued functional integrals generated by the Dirac equation with relativistic Hamiltonian are considered. The Dirac Hamiltonian contains scalar and vector potentials. The sum of the scalar and vector potentials is equal to zero, i.e., the case of pseudospin symmetry is investigated. In this case, a Schrödinger-type equation for the eigenvalues and eigenfunctions of the relativistic Hamiltonian generating the functional integral is constructed. The eigenvalues and eigenfunctions of the Schrödinger-type operator are found using the Sturm sequence method and the reverse iteration method. A method for the evaluation of matrix-valued functional integrals is proposed. This method is based on the relation between the functional integral and the kernel of the evolution operator with the relativistic Hamiltonian and the expansion of the kernel of the evolution operator in terms of the found eigenfunctions of the relativistic Hamiltonian.
About the Authors
Е. A. Ayryan
Laboratory of Information Technologies, Joint Institute for Nuclear Research; State University «Dubna»
Russian Federation
Russian Federation
Edik A. Ayryan – Ph. D. (Physics and Mathematics), Head of Sector
М. Hnatic
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research; Institute of Experimental Physics, Slovak academy of Sciences; Faculty of Sciences, P. J. Šafárik University in Košice
Russian Federation
Russian Federation
Michal Hnatic – Dr. Sc. (Physics and Mathematics), Professor, Deputy Director
6, Joliot-Curie Str., Dubna
47, Watsonova Str., Košice
9, Park Angelinum, Košice
V. В. Malyutin
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Victor B. Malyutin – Dr. Sc. (Physics and Mathematics), Principal Researcher
11, Surganov Str., 220072, Minsk
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