×

zbMATH — the first resource for mathematics

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.

MSC:
46N50 Applications of functional analysis in quantum physics
81P20 Stochastic mechanics (including stochastic electrodynamics)
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.