Prequantization of infinite dimensional dynamical systems (Q1101754)

The paper represents a step in the direction of extending geometric quantization theory from finite dimensions to field theories. The main theorem is an application of the author's tools to the Klein-Gordon equation: In a spatially compact static two-dimensional spacetime, the flow corresponding to the nonlinear Klein-Gordon equation preserves the measure class of a certain Gaussian measure, and lifts to a strongly continuous unitary group on a corresponding Hilbert space. The author uses a Gaussian measure on an abstract Wiener space to play the role of an infinite dimensional volume element replacing the (finite dimensional) Liouville measure.