Geometric prequantization on the path space of a prequantized manifold

TL;DR

This paper develops a geometric prequantization framework for the path space of a prequantized symplectic manifold and applies it to analyze the symplectic structure of solutions to the Klein-Gordon equation.

Contribution

It introduces a novel prequantization method for path spaces of symplectic manifolds and explores its application to quantum field theory.

Findings

Prequantization of path space functions induced by manifold functions.

Application to symplectic structure of Klein-Gordon solutions.

Framework potentially useful for quantum field theory analysis.

Abstract

Given a compact symplectic manifold $M$, with integral symplectic form, we prequantize a certain class of functions on the path space for $M$. The functions in question are induced by functions on $M$. We apply our construction to study the symplectic structure on the solution space of Klein-Gordon equation.