On a Path Integral with a Topological Constraint

In various problems in theoretical physics one has to evaluate a path integral with a constraint which is of a topological nature. This arises, for example, in the theory of polymers or in the analysis of the Aharonov-Bohm effect (see ref. [ 1 ] and the literature quoted therein). In order to elucidate some of these problems Inomata and Singh [2] considered path integrals over trajectories in a plane (with polar coordinates r and 0, 0 < r< oo, 0 < 0 < 2~ ) where the constraint could be expressed a s