  The theme of doing quantum mechanics on all abelian groups goes back to
Schwinger and Weyl. If the group is a vector space of finite dimension over a
non-archimedean locally compact division ring, it is of interest to examine the
structure of dynamical systems defined by Hamiltonians analogous to those
encountered over the field of real numbers. In this letter a path integral
formula for the imaginary time propagators of these Hamiltonians is derived.
