https://doi.org/10.1140/epjc/s10052-022-10374-1
Regular Article - Theoretical Physics
Lorentzian path integral for quantum tunneling and WKB approximation for wave-function
Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, 819-0395, Fukuoka, Japan
a
hiroki.matsui@yukawa.kyoto-u.ac.jp
Received:
15
October
2021
Accepted:
28
April
2022
Published online:
11
May
2022
Recently, the Lorentzian path integral formulation using the Picard–Lefschetz theory has attracted much attention in quantum cosmology. In this paper, we analyze the tunneling amplitude in quantum mechanics by using the Lorentzian Picard–Lefschetz formulation and compare it with the WKB analysis of the conventional Schrödinger equation. We show that the Picard–Lefschetz Lorentzian formulation is consistent with the WKB approximation for wave-function and the Euclidean path integral formulation utilizing the solutions of the Euclidean constraint equation. We also consider some problems of this Lorentzian Picard–Lefschetz formulation and discuss a simpler semiclassical approximation of the Lorentzian path integral without integrating the lapse function.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
