论文标题
用于磁性单极的Feynman-KAC公式
A Feynman-Kac formula for magnetic monopoles
论文作者
论文摘要
我们考虑了在Dirac磁性单极存在下带电粒子的量子力学。波函数是复杂的线束的部分，磁电势是捆绑包上的连接。我们使用连续的本本函数扩展来找到对哈密顿式的基本自我相关性的不变领域。这导致了表达假想时间Schrodinger方程作为随机积分的feynman-kac公式的证明。
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 a Feynman-Kac formula expressing solutions of the imaginary time Schrodinger equation as stochastic integrals.
