New Quantum Electrodynamics for Vector Mesons

Abstract

A quantum electrodynamics for vector mesons with arbitrary magnetic dipole and electric quadrupole moments is constructed in which the vector meson is described by a six-component column matrix satisfying a single equation of motion with no auxiliary condition. To avoid an interaction Hamiltonian which has an infinite number of surface terms, the $S$ matrix is derived directly from Green-function solutions of the equations of motion. In the reduction of the $S$ matrix, terms appear which do not correspond to Feynman-type terms but which vanish if only regularized integrals are used. The Feynman rules are then identical in form to the rules for scalar electrodynamics. A distinct calculational advantage of this theory is that all components of the Fock-space operators are treated on an equal footing and create and destroy particles in definite energy and helicity states. Trace theorems for the covariantly defined spin-1 matrices are given to further facilitate calculations. The same techniques are applied to the electrodynamics of arbitrary-spin particles. A discussion of the renormalization is given: All of the theories are found to be nonrenormalizable.