A Feynman–Kac formula for magnetic monopoles

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Infinite Dimensional Analysis, Quantum Probability and Related Topics

سال: 2021

ISSN: ['0219-0257', '1793-6306']

DOI: https://doi.org/10.1142/s0219025721500156