A generalization of the fourier transform and applications to quantum field theory

Abstract

Using a generalization of the usual Fourier transform on Minkowski space we demonstrate an SO0(l, 4) (SO0(3, 2)) equivalence between a massless spin 0 or spin 1/2 particle on de Sitter space (anti-de Sitter space) and corresponding particles of mass \(- \frac{1}{{4R^2 }}\left( {\frac{1}{{4R^2 }}} \right)or - \frac{2}{{R^2 }}\left( {\frac{2}{{R^2 }}} \right)\), respectively. Using these results we consider an interpretation of Feynman's theory of relativistic cut-off as a theory of interaction of matter with massless virtual bosons in de Sitter or anti-de Sitter space. This interpretation leads to some interesting results about the electromagnetic mass differences of hadrons.