Finite Spectral Quantum Field Theory

Abstract

Using the spectral properties of orthogonal polynomials, we introduce an algebraic version of quantum field theory for elementary particles. Closed-loop integrals in the Feynman diagrams for computing transition amplitudes are divergence-free. Consequently, the theory is finite and no renormalization scheme is required.

Dedicated to the memories of my PhD thesis advisor and friend, the late Christian Fronsdal, who was passionate about sailing his self-built trimaran and playing Go as well as doing mathematical physics