  Based on a recently proposed quantum field theory (QFT) for particles with or
without structure, called "Structural Algebraic QFT (SAQFT)", we introduce a
finite QFT. That is, a QFT for structureless elementary particles that does not
require renormalization where loop integrals in the Feynman diagrams are
finite. It is an algebraic theory utilizing orthogonal polynomials and based on
the structureless sector of SAQFT.
