JournalsprimsVol. 49, No. 1pp. 189–214

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

  • Fumio Hiroshima

    Kyushu University, Fukuoka, Japan

  • Takashi Ichinose

    Kanazawa University, Japan

  • József Lőrinczi

    Loughborough University, UK
Probabilistic Representation and Fall-Off of Bound States of Relativistic Schrödinger Operators with Spin 1/2 cover
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Abstract

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.

Cite this article

Fumio Hiroshima, Takashi Ichinose, József Lőrinczi, Probabilistic Representation and Fall-Off of Bound States of Relativistic Schrödinger Operators with Spin 1/2. Publ. Res. Inst. Math. Sci. 49 (2013), no. 1, pp. 189–214

DOI 10.4171/PRIMS/102