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Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field. (English) Zbl 0606.60060
A rigorous path integral representation of the solution of the Cauchy problem for the pure-imaginary-time Schrödinger equation \(\partial_ 1\psi (t,x)=-[H-mc^ 2]\psi (t,x)\) is established. H is the quantum Hamiltonian associated, via the Weyl correspondence, with the classical Hamiltonian \([(cp-eA(x))^ 2+m^ 2c^ 4]^{1/2}+e\Phi (x)\) of a relativistic spinless particle in an electromagnetic field. The problem is connected with a time homogeneous Lévy process.

60H25 Random operators and equations (aspects of stochastic analysis)
81P20 Stochastic mechanics (including stochastic electrodynamics)
82B10 Quantum equilibrium statistical mechanics (general)
83C50 Electromagnetic fields in general relativity and gravitational theory
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