Covariance and the Feynman Rules of a Massive Gauge Theory

Abstract

If the interaction Lagrangian contains derivatives, or if the spins of the interacting particles ≥ 1, then both the propagators and the interaction Hamiltonian contain normal-dependent terms. Lee and Yang showed that if the noncovariant part of the propagator is dropped, then the finite interaction Hamiltonian is modified. In addition, there appears a term that is divergent, anti-Hermitian, and generally noncovariant if it does not vanish, namely, $\delta H=\frac{1}{2}i\hslash {\delta }^4\mathrm{}\left(0\right)\mathrm{}\times \ln \det g$, where $g$ depends on the structure of the theory. For massive gauge theories we have shown that $\delta H=0\mathrm{}$ and that $H_{\mathrm{int}}=-L_{\mathrm{int}}$. These theories are manifestly covariant and the ordinary Feynman rules hold. Renormalization is not discussed.