Functional Integration on Constrained Function Spaces II: Applications

TL;DR

This paper explores the use of conditional integrators in quantizing constrained quantum systems, offering new insights and applying the formalism to model prime counting functions as a constrained gamma process.

Contribution

It introduces the notion of conditional integrators for constrained systems and applies this to model prime counting functions, providing novel perspectives on existing quantum quantization methods.

Findings

Re-examination of constrained quantum systems using conditional integrators

New perspectives on classical results in quantum mechanics

Modeling of prime counting functions as a constrained gamma process

Abstract

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.