Self-reciprocal fermion mass ratios from massless QED with curved momentum space

The present investigation is an attempt to understand the fermion mass ratios in the framework of QED of charged fermions without a bare mass. Since QED of massless charged fermions is invariant under the dilatation transformation, this symmetry has to be spontaneously broken to obtain massive fermions. In the proposed model we combine a mass-scale normalisation with the renormalisation procedure, assuming the fermion momentum space being a four-dimensional one-shell hyperboloid embedded in a five-dimensional space. The hyperboloid constrains the allowed fermion field solutions. We construct the theory in the conventional way using equal time anti-commutator and the Lagrangian formalism. Starting from the Dyson–Schwinger equation for fermion propagator in the Landau gauge, we derive the fermion mass function and self-reciprocal solutions for the mass ratios, which are independent of any constant.