The path integral and ordering of noncommuting operators

Abstract

It is well known that the ambiguity resulting from ordering noncommuting operators is connected with the ambiguity of the lattice approximation of the path integral (PI), When PI quantization is used. We show that for H = 1 2 g ij (q)p ip j + V(q) the ordering is uniquely defined by construction of the PI. A different lattice approximation defines a different ΔV in the action. It reflects the ambiguity in writing H  1 2 g − 1 4 (q)p ig ij(q)g 1 2 p jg(q) − 1 4 = H F + ΔV F , where the subscript F stands for the specific choice of ordering, e.g., Weyl ordering, p̂q̂-ordering, etc.