The discrete Feynman integral.

We construct a genuine Radon measure with values in B(ℓ2(Zd)) on the set of paths in Zd representing Feynman’s integral for the discrete Laplacian on ℓ2(Zd), and we prove the Feynman integral formula for the solutions of the Schrödinger equation with Hamiltonian H=-<FRACTION><NUM>1</NUM><DEN>2</DEN></FRACTION>Δ+V, where Δ is the discrete Laplacian and V is an arbitrary bounded potential. [ABSTRACT FROM AUTHOR]