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Lévy flights and nonlocal quantum dynamics. (English) Zbl 1284.81012
Summary: We develop a fully fledged theory of quantum dynamical patterns of behavior that are nonlocally induced. To this end we generalize the standard Laplacian-based framework of the Schrödinger picture quantum evolution to that employing nonlocal (pseudodifferential) operators. Special attention is paid to the Salpeter (here, \(m \geq 0\)) quasirelativistic equation and the evolution of various wave packets, in particular to their radial expansion in 3D. Foldy’s synthesis of ”covariant particle equations” is extended to encompass free Maxwell theory, which however is devoid of any ”particle” content. Links with the photon wave mechanics are explored.
©2013 American Institute of Physics

MSC:
81P05 General and philosophical questions in quantum theory
60G51 Processes with independent increments; Lévy processes
35S05 Pseudodifferential operators as generalizations of partial differential operators
81Q40 Bethe-Salpeter and other integral equations arising in quantum theory
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
81V80 Quantum optics
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