Probabilistic Representation and Fall-Off of Bound States of Relativistic Schrödinger Operators with Spin 1/2 | Zendy

Fumio Hiroshima | Zendy; Takashi Ichinose | Zendy; József Lőrinczi | Zendy

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Probabilistic Representation and Fall-Off of Bound States of Relativistic Schrödinger Operators with Spin 1/2

Author(s) -

Fumio Hiroshima,

Takashi Ichinose,

József Lőrinczi

Publication year - 2013

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.4171/prims/102

Subject(s) - mathematics , probabilistic logic , spin (aerodynamics) , representation (politics) , schrödinger's cat , mathematical physics , physics , statistics , political science , thermodynamics , politics , law

A Feynman-Kac type formula for relativistic Schrödinger operators with unbounded vector potential and spin 1=2 is given in terms of a three-component process consisting of a Brownian motion, a Poisson process and a subordinator. This formula is obtained for unbounded magnetic fields and magnetic fields with zeros. From this formula an energy comparison inequality is derived. Spatial decay of bound states is established separately for growing and for decaying potentials by using martingale methods. © 2013 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved

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