Operator ordering and Feynman rules in gauge theories

Abstract

The ordering of operators in the Yang-Mills Hamiltonian is determined for the ${V}_{0}=0$ gauge and for a general noncovariant gauge $\ensuremath{\chi}({V}_{i})=0$, with $\ensuremath{\chi}$ a linear function of the spatial components of the gauge field ${V}_{\ensuremath{\mu}}$. We show that a Cartesian ordering of the ${V}_{0}=0$ gauge Hamiltonian defines a quantum theory equivalent to that of the usual, covariant-gauge Feynman rules. However, a straightforward change of variables reduces this ${V}_{0}=0$ gauge Hamiltonian to a $\ensuremath{\chi}({V}_{i})=0$ gauge Hamiltonian with an unconventional operator ordering. The resulting Hamiltonian theory, when translated into Feynman graphs, is shown to imply new nonlocal interactions, even in the familiar Coulomb gauge.