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Communications in Mathematical Physics

, Volume 105, Issue 2, pp 239–257 | Cite as

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

  • Takashi Ichinose
  • Hiroshi Tamura
Article

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−mc2]ψ(t,x) is established.H is the quantum Hamiltonian associated, via the Weyl correspondence, with the classical Hamiltonian [(cp−eA(x))2+m2c4]1/2+eΦ(x) of a relativistic spinless particle in an electromagnetic field. The problem is connected with a time homogeneous Lévy process.

Keywords

Neural Network Statistical Physic Complex System Cauchy Problem Electromagnetic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Takashi Ichinose
    • 1
  • Hiroshi Tamura
    • 2
  1. 1.Department of MathematicsKanazawa UniversityKanazawaJapan
  2. 2.Department of PhysicsHokkaido UniversitySapporoJapan

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