A Feynman–Kac formula for magnetic monopoles

J. Dimock

doi:10.1142/S0219025721500156

A Feynman–Kac formula for magnetic monopoles

J. Dimock

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 Schrödinger equation as stochastic integrals.

Original language	English
Article number	2150015
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	24
Issue number	2
DOIs	https://doi.org/10.1142/S0219025721500156
State	Published - Jun 2021

Keywords

Feynman–Kac
Magnetic monopole
Schrödinger operator
U(1) vector bundle

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10.1142/S0219025721500156

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AB - 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 Schrödinger equation as stochastic integrals.

KW - Feynman–Kac

KW - Magnetic monopole

KW - Schrödinger operator

KW - U(1) vector bundle

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M3 - Article

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IS - 2

M1 - 2150015

ER -

A Feynman–Kac formula for magnetic monopoles

Abstract

Keywords

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