Fourier transformation of a class of hyperfunctions and formulation of the condition of local commutativity in the framework of localizable quantum field theory in terms of hyperfunctions
Abstract:
Theory of hyperfunctions is used for the formulation of aximatic local quantum
field theory. Class $\mathscr L$ of hyperfunctions is introduced, which are local in coordinate
as well as in the momentum space. Direct and inverse Fourier transformation of the
hyperfunctions of the class $\mathscr L$ is defined and the relation of these hyperfunctions to
generalized functions from the space $S_1{}^{1^\prime}$ is established. On the basis of notion of
support of the hyper function the locality axiom is formulated for localizable field
theories.