Coherent-state path integral operator ordering, and regularization: A simple example

Abstract

For a restricted class of potential problems, the Feynman path integral in the coordinate representation circumvents operator-ordering ambiguities. We will show that, in the coherent-state representation, the traditional continuum time path integral cannot resolve this issue. Using a simple solvable model, we carry out a careful analysis of the continuum limit with regularization. The latter is found to be necessary to address the operator-ordering issue.