Path integrals on finite sets (Q1914897)

The author uses the formalism of the Feynman path integral to ``solve'' \[ -{1 \over i} {\partial \over \partial t} \phi_t = H_0 \phi_t \] where \(H_0\) is a self-adjoint operator on \(L^2(M) = \mathbb{C}^M\), \(M\) being a finite set. The paths are functions of \(\mathbb{R}\) with values in \(M\). The path integral here is a family of measures parametrized by \(t'\) and \(t\) with values in the space of operators on \(L^2(M)\). The relationship of these measures to the measures of a Markov process is studied and it is shown that these measures are concentrated on a certain set of step measures. Some applications to certain hypothetical systems are also considered.