The Feynman path integral for constrained systems

Steven K. Blau

J. LaChapelle

Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As an interesting new application, the formalism is used to construct a physical model of average prime counting functions modeled as a constrained gamma process.

Bung-Ning Teng

J. Iliopoulos, Theodore N. Tomaras

Abstract In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.

Cécile DeWitt-Morette