Geometric prequantization on the path space of a prequantized manifold

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.

24 pages,[accepted]. appears in International Journal of Geometric Methods in Modern Physics (2014)

References in corpus (2)

• Parallel Transport over Path Spaces
• Negative forms and path space forms