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Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field
Authors:Takashi Ichinose  Hiroshi Tamura
Institution:(1) Department of Mathematics, Kanazawa University, 920 Kanazawa, Japan;(2) Department of Physics, Hokkaido University, 060 Sapporo, Japan
Abstract:A rigorous path integral representation of the solution of the Cauchy problem for the pure-imaginary-time Schrödinger equation piv t psgr(t, x)=–H–mc 2]psgr(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+ePHgr(x) of a relativistic spinless particle in an electromagnetic field. The problem is connected with a time homogeneous Lévy process.
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