Parametrization of Ordering Ambiguity and Its Representation in Path Integral Formalism

Abstract

In this paper, we establish three different types (type I, type II and type III) of parametrization of ordering ambiguity in operator formalism of quantum mechanics and discuss their nontrivial relations. Some commonly occurred bewilderment about ordering problem is made clear. We also show that the ordering ambiguity exists in path intergral formalism and the representation of the ordering ambiguity in the path integral formalism (discrete schemes) has a one-to-one correspondence with type II parametrization of the ordering ambiguity in the operator formalism. As a result, we show that to select a physically a misled attempt. Instead, we have to work with type III parametrization in the operator formalism to reduce the ordering ambiguity by physical requirements.