Bulgarian Journal of Physics  15 (1988) 323-333

Stochastic Quantization and Geometry of Quantum Phase Space

           B.A. Nikolov,  D.A. Trifonov
 
 

Abstract. - A geometrical approach to the stochastic quantization is presented and
a notion of quantum phase space is introduced. In this approach the highly reducible
representation generated by Wigner-Bopp-like operators appears as an action of
appropriately extended group of phase space translations on a fibre bundle based
on the phase space. The structure of quantum phase space depends on a certain
test particle wave function which in turn determines a Riemannian metrics in phase
space as well as the corresponding quantization rules.

    A generalized stochastic quantization is suggested to account for the influence of
the classical measuring device and the connection to Agarwal-Wolf quantization rules
is established.
 
 
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