The semiclassical approximation of multiple functional integrals
Victor MalyutinInstitute of Mathematics of the National Academy of Sciences of BelarusB. O. NurjanovInstitute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan;
Karakalpak State University named after Berdakh
Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Seriesjournal2024en
ABI
Abstract
In this paper, we study the semiclassical approximation of multiple functional integrals. The integrals are defined through the Lagrangian and the action. Of all possible trajectories, the greatest contribution to the integral is given by the classical trajectory x̅ cl for which the action S takes an extremal value. The classical trajectory is found as a solution of the multidimensional Euler – Lagrange equation. To calculate the functional integrals, the expansion of the action with respect to the classical trajectory is used, which can be interpreted as an expansion in powers of Planck’s constant. The numerical results for the semiclassical approximation of double functional integrals are given.
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