The Path Integral Formalism

Taku Goto, S. Naka

An operator formalism to the path integral method is developed. In this formalism the operator characterizing the trajectories of the particle is introduced and the usual path integral is expressed in terms of expectation value of a functional of that operator. We also investigate the Wiener-Hermite expansion on the basis of our operator formalism. Feynman's path integral is justified as a sort of analytic continuation of the path integral in the Wiener process.

John A. Colosi

M.-a. Sato

The operator ordering problem in the path integral formalism is studied in the context of the perturbation expansion. For a given ordered Hamiltonian, there exists a path integral formula which reproduces the corresponding quantum mechanics, i.e., the same Feynman­ Wick rules as the operator formalism. The Weyl ordering is shown to play an important role in connecting the discrete path integral (defined on a finite mesh) with the continuous one.

Leon W. Cohen

Ioan Zaharie, Viorel Laurentiu Cartas

In this paper we apply the path integral formalism for the quantum rigid rotator in 2+1 space time dimension related to the knot theory. The knots theory put the knots into an one to one relation with the braids considered in the braid group theory where braids are actually path into the path integrals formalism. The present work aims the connection between such theories and the anyons behavior.