Massive Yang-Mills fields

Abstract

Two problems are studied in the paper: (i) the relation between Lagrangian and Feynman rules if the Lagrangian contains derivative couplings and/or vector meson fields and (ii) the behaviour of certain two closed loop diagrams in the perturbation theory of Yang-Mills fields. With respect to (i), using an extremely simple regularisation procedure, the canonical formalism is shown to give directly manifestly covariant Feynman rules. With respect to (ii), a certain set of Feynman rules involving ghost particles is known to be valid for diagrams of the Yang-Mills theory with no or one close loop. It is shown however that with the same set of rules the imaginary part of the two-loop self-energy diagrams receives a non-zero contribution of the unphysical three-ghost intermediate state.