Class Of Fock Spaces Research Articles

Fourier transforms in generalized Fock spaces

A classical Fock space consists of functions of the form, urn:x-wiley:01611712:media:ijmm629657:ijmm629657-math-0001 where ϕ0 ∈ C and ϕq ∈ L2(R3q), q ≥ 1. We will replace the ϕq, q ≥ 1 with q‐symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.

A class of conformally invariant quantum field theories

A general family of two-dimensional field theories of the Liouville type, involving one or more scalar fields, is shown to be conformally invariant when quantized canonically over a large class of Fock spaces.