Abstract

We consider, on one hand, Segal's geometric quantization scheme which is formulated on a non-linear configuration-space manifold M and, on other, Van Hove's solution of the quantization mapping with an inherent phase space content. We furnish geometrical interpretations for Van Hove's solution with respect to both M and its cotangent bundle T∗(M) (phase space). In the latter case, we are able to introduce commutation relations which extend Segal's scheme in the direction suggested by Van Hove's mapping.

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