The effect of time changes on Feynman\u27s operational calculus as made rigorous by Wiener and Feynman integrals

It is known that Wiener and Feynman path integrals provide one way of making Feynman\u27s heuristic operational calculus for noncommuting operators mathematically rigorous. The disentangling process and associated operator orderings are central to Feynman\u27s ideas. Motivated by the use of the time reversal map by Johnson and Lapidus in putting generalized Dyson series in natural physical order, we begin here to study the effects of time maps in clarifying the disentangling process and in altering the operator orderings in certain prescribed ways. Further, we discuss the settings in which the path integral approach and Feynman\u27s heuristic rules give the same results. These connections allow us to extend the class of evolution equations that can be solved within the path integral setting, that is, the setting where Feynman\u27s operational calculus is made rigorous by Wiener and Feynman integrals