Remarks on the Feynman Representation

Abstract

It is shown that there exists a complete space ∂L¹(M_t^K, M_t^D) of integrable functions such that for any potential V with zero H₀-bound relative to the free Hamiltonian operator H₀ of a finite non-relativistic quantum system, the function exp[−i∫₀^tV{\circ}X_sds] belongs to ∂L¹(M_t^K, M_t^D), and the Feynman representation e^{−i(H₀+V)t}=∫_Ωexp[−i∫₀^tV{\circ}X_sds] dM_t^F is valid.