Quantum Field Theory in Terms of Fourier Hyperfunctions

Abstract

The Wightman axioms are extended to the quantum field theory in terms of Fourier hyperfunctions. The support concept of hyperfunctions is crucial for the formulation of locality and spectral condition. The complete equivalence is proved between modified Wightman axioms for relativistic theory and modified Osterwalder–Schrader axioms for Euclidean theory.