On the electron-muon mass ratio

The quantum electrodynamics (QED) of electrons is considered as a theory with a passive dilatation invariance which is perturbed by the electromagnetic coupling to hadrons and muons. A stability criterium is introduced and evaluated in lowest order of the perturbation. The resulting expression for the electron-muon mass ratio in terms of the vacuum polarization can be tested in e+ − e− colliding beam experiments

Renormalization and gauge invariance in quantum electrodynamics

The connection between the field theory and the perturbation expansion of quantum electrodynamics is studied. As a starting point the usual Lagrangian is taken but with bare electron mass and the renormalization constant Z3 set equal to zero. This theory is essentially equivalent to the usual one; however, it does not contain any constant of nature and is dilatational and gauge invariant, both invariances being spontaneously broken. The various limiting procedures implied by the differentiation, the multiplication and the renormalization of the field operators in the Lagrangian are combined in a gauge invariant way to a single limit. Propagator equations are derived which are the usual renormalized ones, except for: (i) a natural cancellation of the quadratic divergence of the vacuum polarization; (ii) the presence of an effective cutoff at p ≈ ϵ−1; (iii) the replacement of the renormalization constants Z1 and Z2 by one gauge dependent function Z(ϵ2); (iv) the limit ϵ → 0 which has to be taken. The value Z(0) corresponds to the usual constants Z1 and Z2. It is expected that in general Z(0) = 0, but this poses no problem in the present formulation. It is argued that the function Z(ϵ2), which is determined by the equations, may render the vacuum polarization finite. One may eliminate the renormalization function from the propagator equations and then perform the limit ϵ → 0; this results in the usual perturbation series. However, the renormalization function is essential for an understanding of the high momentum behaviour and of the relation between the field theory and the perturbation expansion

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

Degrees of symmetry in quantum field theories

A hierarchy of possible symmetries in quantum field theory is defined, which reaches from a purely mathematical invariance to the conventional physical invariance, including the commonly discussed type of spontaneously broken symmetry (SBS). It is shown that one type of SBS, which is usually not considered, naturally leads to theories with an algebra of non-conserved currents and a non-linearly transforming phenomenological Lagrangian. An exactly solvable model is given and some general remarks are made

Charge commutator for any momentum

The nucleon matrix elements of the charge commutation relations are considered for arbitrary momentum. The resulting expression is exact. The high-momentum limit reduces to the Alder-Weisberger sum rule. For zero momentum one obtains the known low-energy result together with a closed expression for the correction

On the electron-muon mass ratio

The quantum electrodynamics (QED) of electrons is considered as a theory with a passive dilatation invariance which is perturbed by the electromagnetic coupling to hadrons and muons. A stability criterium is introduced and evaluated in lowest order of the perturbation. The resulting expression for the electron-muon mass ratio in terms of the vacuum polarization can be tested in e+ − e− colliding beam experiments