Approximate Calculation of Functional Integrals Generated by Nonrelativistic and Relativistic Hamiltonians-Reference-Cited by-同舟云学术

Approximate Calculation of Functional Integrals Generated by Nonrelativistic and Relativistic Hamiltonians

Published:2023-09-18 Issue:9 Volume:15 Page:1785
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Ayryan Edik¹²³,Hnatic Michal⁴⁵⁶,Honkonen Juha⁷⁸^ORCID,Malyutin Victor⁹

Affiliation:

1. Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Russia

2. Institute of System Analysis and Management, Dubna State University, 141982 Dubna, Russia

3. A.I. Alikhanyan National Science Laboratory, Yerevan 0036, Armenia

4. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

5. Institute of Experimental Physics, Slovak Academy of Sciences, 04001 Košice, Slovakia

6. Faculty of Sciences, P.J. Šafárik University in Košice, 04001 Košice, Slovakia

7. Department of Military Technology, National Defence University, 00860 Helsinki, Finland

8. Department of Physics, University of Helsinki, 00014 Helsinki, Finland

9. Institute of Mathematics of the National Academy of Sciences of Belarus, 220072 Minsk, Belarus

Abstract

The discussion revolves around the most recent outcomes in the realm of approximating functional integrals through calculations. Review of works devoted to the application of functional integrals in quantum mechanics and quantum field theory, nuclear physics and in other areas is presented. Methods obtained by the authors for approximate calculation of functional integrals generated by nonrelativistic Hamiltonians are given. One of the methods is based on the expansion in eigenfunctions of the Hamiltonian. In an alternate approach, the functional integrals are tackled using the semiclassical approximation. Methods for approximate evaluation of functional integrals generated by relativistic Hamiltonians are presented. These are the methods using functional polynomial approximation (analogue of formulas of a given degree of accuracy) and methods based on the expansion in eigenfunctions of the Hamiltonian, generating a functional integral.

Funder

VEGA

Russian Science Foundation

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/9/1785/pdf

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4. Roepstorff, G. (1994). Path Integral Approach to Quantum Physics: An Introduction, Springer.

5. Bogoliubov, N.N., and Shirkov, D.V. (1980). Introduction to the Theory of Quantized Fields, John Wiley & Sons. [3rd ed.].