Proceedings of the Japan Academy, Series A, Mathematical Sciences

The zero-mass limit problem for a relativistic spinless particle in an electromagnetic field

Takashi Ichinose and Taro Murayama

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Abstract

It is shown that mass-parameter-dependent solutions of the imaginary-time magnetic relativistic Schrödinger equations converge as functionals of Lévy processes represented by stochastic integrals of stationary Poisson point processes if mass-parameter goes to zero.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 3 (2014), 60-65.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.pja/1393510217

Digital Object Identifier
doi:10.3792/pjaa.90.60

Mathematical Reviews number (MathSciNet)
MR3178487

Zentralblatt MATH identifier
1298.82033

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 60F17: Functional limit theorems; invariance principles 60H05: Stochastic integrals 35S10: Initial value problems for pseudodifferential operators 81S40: Path integrals [See also 58D30]

Keywords
Magnetic relativistic Schrödinger operator imaginary-time relativistic Schrödinger equation Lévy process path integral formula Feynman-Kac-Itô formula

Citation

Ichinose, Takashi; Murayama, Taro. The zero-mass limit problem for a relativistic spinless particle in an electromagnetic field. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 3, 60--65. doi:10.3792/pjaa.90.60. https://projecteuclid.org/euclid.pja/1393510217


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