Violations of dimensional analysis in renormalized perturbation theory

Abstract

The Green's functions of renormalizable quantum field theory are shown to violate, in general, Euler's theorem on homogeneous functions, that is to say, to violate naive dimensional analysis. The respective violations are established by explicit calculation with Feynman diagrams. These violations, when incorporated into the renormalization group, may provide the basis for an entirely new approach to asymptotic behavior in renormalizable field theory.