Feynman formulas generated by self-adjoint extensions of the Laplacian

Abstract

A Feynman formula is a representation of the Schrodinger group or the Schrodinger semigroup by using limits of integrals over Cartesian powers of some space E . Here, H is a classical Hamiltonian and is a quantum mechanical Hamiltonian, which is a self-adjoint extension of a (pseudo)differential operator with the symbol H . If E is the phase or configuration space of a classical Hamiltonian system, we have a Feynman formula in the corresponding space. The multiple integrals in Feynman formulas approximate integrals with respect to some measures or pseudomeasures on the set of E -valued functions defined on a real interval (such functions are called trajectories in E ). A