Abstract
The problem of prequantization of infinite dimensional dynamical systems is considered, using a Gaussian measure on an Abstract Wiener Space to play the role of volume element replacing the Liouville measure. As an example, it is shown that the flow on L 1 2(Ω) × L 0 2(Ω) corresponding to the nonlinear Klein-Gordon field over a two dimensional static space time N=Ω × R leaves the Gaussian measure defined on this space w.r.t. the norm on L s + 1 2 × L s 2 (where 1 2 < s < 1) quasi-invariant. This makes it possible to carry out the prequantization in this case.
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