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Hamiltonian Feynman path integrals via the Chernoff formula. (English) Zbl 1060.58009
Summary: The main aim of the present paper is using a Chernoff theorem (i.e., the Chernoff formula) to formulate and to prove some rigorous results on representations for solutions of Schrödinger equations by the Hamiltonian Feynman path integrals (= Feynman integrals over trajectories in the phase space). The corresponding theorem is related to the original (Feynman) approach to Feynman path integrals over trajectories in the phase space in much the same way as the famous theorem of Nelson is related to the Feynman approach to the Feynman path integral over trajectories in the configuration space. We also give a representation for solutions of some Schrödinger equations by a series which represents an integral with respect to the complex Poisson measure on trajectories in the phase space.

58D30 Applications of manifolds of mappings to the sciences
46G12 Measures and integration on abstract linear spaces
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
81S40 Path integrals in quantum mechanics
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