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 stochast...

We give sufficient conditions for the essential self-adjointness of perturbed biharmonic operators acting on sections a Hermitian vector bundle over Riemannian manifold with additional assumptions, such as lower semi-bounded Ricci curvature or bounded sectional curvature. In case curvature, we formulate our results in terms completeness metric that is conformal to original one, via factor depen...