Lorentzian path integral for quantum tunneling and WKB approximation for wave-function

• URL: http://arxiv.org/abs/2102.09767v4
• Date: Fri, 15 Oct 2021 10:37:52 GMT
• Title: Lorentzian path integral for quantum tunneling and WKB approximation for wave-function
• Authors: Hiroki Matsui
• Abstract summary: We show that the Picard-Lefschetz Lorentzian formulation is consistent with the WKB approximation for wave-function. We discuss a simpler semiclassical approximation of the Lorentzian path integral without integrating the lapse function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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