A Feynman-Kac formula for magnetic monopoles

被引：0

作者：

Dimock, J. ^{[1
]}

机构：

[1] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2021年 / 24卷 / 02期

关键词：

Magnetic monopole; U(1) vector bundle; Feynman-Kac; Schrodinger operator;

D O I：

10.1142/S0219025721500156

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the quantum mechanics of a charged particle in the presence of Dirac's magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum eigenfunction expansion to find an invariant domain of essential self-adjointness for the Hamiltonian. This leads to a proof of the Feynman-Kac formula expressing solutions of the imaginary time Schrodinger equation as stochastic integrals.

引用

页数：18

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