Two-dimensional Yang-Mills theory in the leading 1/N expansion revisited

We obtain a formal solution of an integral equation for $q\bar q$ bound states, depending on a parameter \eta which interpolates between 't Hooft's (\eta=0) and Wu's (\eta=1) equations. We also get an explicit approximate expression for its spectrum for a particular value of the ratio of the coupling constant to the quark mass. The spectrum turns out to be in qualitative agreement with 't Hooft's as long as \eta \neq 1. In the limit \eta=1 (Wu's case) the entire spectrum collapses to zero, in particular no rising Regge trajectories are found.Comment: CERN-TH/96-364, 13 pages, revTeX, no figure

Split Dimensional Regularization for the Coulomb Gauge

A new procedure for regularizing Feynman integrals in the noncovariant Coulomb gauge is proposed for Yang-Mills theory. The procedure is based on a variant of dimensional regularization, called split dimensional regularization, which leads to internally consistent, ambiguity-free integrals. It is demonstrated that split dimensional regularization yields a one-loop Yang-Mills self-energy that is nontransverse, but local. Despite the noncovariant nature of the Coulomb gauge, ghosts are necessary in order to satisfy the appropriate Ward/BRS identity. The computed Coulomb-gauge Feynman integrals are applicable to both Abelian and non-Abelian gauge models. PACS: 11.15, 12.38.CComment: 19 pages, 2 figures, 1 table, 72 references. This Replaced version clarifies why the Coulomb gauge requires a new type of regularization, and why our new regularization is compatible with Wick rotation. Results and table of integrals are unchanged. To appear in Nuclear Physics