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.
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页数：18
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