Lorentzian path integral for quantum tunneling and WKB approximation for wave-function
Abstract
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 Schr\"{o}dinger 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.
Keywords
Cite
@article{arxiv.2102.09767,
title = {Lorentzian path integral for quantum tunneling and WKB approximation for wave-function},
author = {Hiroki Matsui},
journal= {arXiv preprint arXiv:2102.09767},
year = {2022}
}
Comments
14 pages, 14 figures; fixed typos, added figures, updated discussion