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


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.


Neural Network Statistical Physic Complex System Cauchy Problem Electromagnetic Field 
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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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