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Stochastic mechanics of a relativistic spinless particle. (English) Zbl 0712.46041
Summary: An extension of Nelson’s stochastic mechanics to the relativistic domain is proposed. To each pure state of a spinless relativistic quantum particle corresponds a Markov process \(t\mapsto \xi_ t\), where the random variable \(\xi_ t\) represents, at every time t, the space position of the particle in the sense of Newton and Wigner. The process \(t\mapsto \xi_ t\) is not a diffusion but the usual Nelson’s theory is restored in the nonrelativistic limit.

46N50 Applications of functional analysis in quantum physics
81P20 Stochastic mechanics (including stochastic electrodynamics)
Full Text: DOI
[1] DOI: 10.1007/BF02770538 · doi:10.1007/BF02770538
[2] Serva M., Ann. Inst. Henri PoincarĂ© 49 pp 415– (1988)
[3] DOI: 10.1103/RevModPhys.20.367 · Zbl 1371.81126 · doi:10.1103/RevModPhys.20.367
[4] DOI: 10.1103/PhysRev.150.1079 · doi:10.1103/PhysRev.150.1079
[5] DOI: 10.1103/RevModPhys.21.400 · Zbl 0036.26704 · doi:10.1103/RevModPhys.21.400
[6] DOI: 10.1103/RevModPhys.34.845 · doi:10.1103/RevModPhys.34.845
[7] DOI: 10.1007/BF01211101 · Zbl 0606.60060 · doi:10.1007/BF01211101
[8] DOI: 10.1088/0305-4470/15/7/016 · doi:10.1088/0305-4470/15/7/016
[9] DOI: 10.1007/BF01218757 · Zbl 0607.60025 · doi:10.1007/BF01218757
[10] DOI: 10.1007/BF01224827 · Zbl 0558.60059 · doi:10.1007/BF01224827
[11] DOI: 10.1063/1.523359 · Zbl 0368.60091 · doi:10.1063/1.523359
[12] DOI: 10.1088/0305-4470/19/6/017 · Zbl 0615.60076 · doi:10.1088/0305-4470/19/6/017
[13] DOI: 10.1007/BF01041607 · Zbl 0709.60560 · doi:10.1007/BF01041607
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