PHASE TRANSITION IN RIGID QED

Abstract

We present a new model of QED which exhibits two distinct phases. The model emerges in the first-quantized formalism where it is possible to generalize QED by adding the curvature of the world line to the usual kinetic term, the arc length action of the point particle. The Boltzmann factor associated with the curvature term favors rigid paths. The curvature term is not only scale-invariant and hence renormalizable but it is also the unique reparametrization-invariant term with second derivatives with this property. The new term transforms a single electron of mass m into an infinite number of particles with masses varying inversely with the spin (Majorana mass spectrum). The value of the bare curvature coupling determines which phase the theory is in. For bare curvature coupling α0 less than a certain critical coupling αc, we recover conventional QED as one phase where the curvature term is absent at large distance scales in the continuum theory. For α0 greater than αc, we have a new phase characterized by a curvature law. Using mean field theory methods, we determine αc to be of the order of one. We argue that the positronium spectrum in the strong curvature phase is approximately described by a Majorana mass formula. Even though the GSI experiments might not survive further experimental tests, we nevertheless examine the Majorana spectrum with the three observed narrow e+ e− peaks observed in the GSI experiments and make some possible new predictions.