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On mapping approaches in axiomatic quantum field theory

A quantum electrodynamics for vector mesons with arbitrary magnetic dipole ancl electric quadrupole moments is co~lstructed 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 Grecn-function solutions of the equations oi motion. I n the reduction of the S matrix, terms appear vhich 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 170ck-space operators are treated on an equal footing and create and destroy particles in definite energy and hclicity states. Trace theorems lor the covariantly defined spin-1 matrices are given to further facilitate calculations. The same techniques are applied to the electrodynamics of arbitrary-spin particles.h discussion of the renormalization is given: All of the theories are found to be nonrenormalizable.

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The Dirac equation, the Weaver-Hammer-Good wave equations, and the Weinberg wave equations are written in a manifestly covariant form in terms of hyperplane parameters according to Fleming's hyperplane formalism. A Fody-Wouthuysen-type wave equation is developed for the Weinberg theory and it, along with the usual Foldy-Wouthuysen wave equation and transformation, is also written in a manifestly covariant form for all spin. Fleming's formalism is extended to include the case where the hyperplane parameters are operators as well as c numbers. As a consequence, a hyperplane observer which corresponds to the particle rest frame is considered, with the result that wave equations are obtained in the usual manifestly covariant form for all spin with no auxiliary conditions or unphysical solutions.