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Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field

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Abstract

A rigorous path integral representation of the solution of the Cauchy problem for the pure-imaginary-time Schrödinger equation ϖ t ψ(t, x)=−[H−mc 2]ψ(t,x) is established.H is the quantum Hamiltonian associated, via the Weyl correspondence, with the classical Hamiltonian [(cp−eA(x))2+m 2 c 4]1/2+eΦ(x) of a relativistic spinless particle in an electromagnetic field. The problem is connected with a time homogeneous Lévy process.

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Authors and Affiliations

  1. Department of Mathematics, Kanazawa University, 920, Kanazawa, Japan

    Takashi Ichinose

  2. Department of Physics, Hokkaido University, 060, Sapporo, Japan

    Hiroshi Tamura

Authors
  1. Takashi Ichinose
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  2. Hiroshi Tamura
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Communicated by H. Araki

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Ichinose, T., Tamura, H. Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field. Commun.Math. Phys. 105, 239–257 (1986). https://doi.org/10.1007/BF01211101

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  • DOI: https://doi.org/10.1007/BF01211101

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