1112.1134 (Rene Angeles-Martinez et al.)

Renormalization of the QED of second order spin 1/2 fermions    [PDF]

Rene Angeles-Martinez, Mauro Napsuciale

In this work we study the renormalization of the electrodynamics of spin 1/2
fermions in the Poincar\'e projector formalism which is second order in the
derivatives of the fields. We analyze the superficial degree of divergence of
the vertex functions of this theory, calculate at one-loop level the vacuum
polarization, fermion self-energy and \gamma-fermion-fermion vertex function
and the divergent piece of the one-loop contributions to the
\gamma-\gamma-fermion-fermion vertex function. It is shown that these functions
are renormalizable independently of the value of the gyromagnetic factor g
which is a free parameter of the theory. We find a photon propagator and a
running coupling constant \alpha (q^2) that depend on the value of g. The
magnetic moment form factor contains a divergence associated to g which
disappears for g=2 but in general requires the coupling g to be renormalized. A
suitable choice of the renormalization condition for the magnetic form factor
yields the one loop finite correction \Delta{g}=g\alpha/2\pi. For a particle
with g=2 we recover results of Dirac theory for the photon propagator, the
running of \alpha (q^2) and the one-loop corrections to the gyromagnetic
factor.

View original: http://arxiv.org/abs/1112.1134