Continuous tensor products of hilbert spaces and generalized random fields

Abstract

The infinite tensor product is generalized to a tensor product of certain Hilbert spaces over a topological index set. The criterion for positivity of characteristic functionals of generalized random processes is used to construct two distinct types of continuous tensor products. Representations of the canonical commutation relations (CCR) are constructed in one of these. The other is seen to be useful in the construction of certain quantum fields.