Functional Integration on Constrained Function Spaces I: Foundations

TL;DR

This paper introduces a novel framework for functional integration on constrained spaces, inspired by Bayesian inference, providing new tools for analyzing constrained dynamical systems.

Contribution

It develops a Bayesian-inspired analogy for functional integrators, leading to new methods for constrained functional integration in dynamical systems.

Findings

Introduces functional counterparts of conditional and conjugate distributions.

Develops new functional integration tools for constrained systems.

Provides a foundation for future applications in constrained dynamical analysis.

Abstract

Analogy with Bayesian inference is used to formulate constraints within a scheme for functional integration proposed by Cartier and DeWitt-Morette. According to the analogy, functional counterparts of conditional and conjugate probability distributions are introduced for integrators. The analysis leads to some new functional integration tools and methods that can be applied to the study of constrained dynamical systems.