OPTIMIZED DELTA-EXPANSION FOR LATTICE U(1) AND SU(2) WITH INTERPOLATING CONTINUUM ACTION

Embedding the lattice gauge theory into a continuum theory allows to u se the continuum action as trial action in the variational calculation . Only originally divergent graphs contribute. This leads to a very si mple scheme which makes it possible to write down explicit expressions for the plaquette energy E for U(1) in arbitrary space time dimension for the first three orders of the expansion. For dimensions three and four one can even go up to fourth order. This allows a rather thoroug h empirical investigation of the convergence properties of the delta-e xpansion, in particular near the phase transition or the transition re gion, respectively. As already found in previous work, the principle o f minimal sensitivity can be only applied for beta above a certain val ue, because otherwise no extremum with respect to the variational para meter exists. One can, however, extend the range of applicability down to small beta, by calculating instead of E some power E(K), or by per forming an appropriate Pade transformation. We find excellent agreemen t with the data for beta above the transition region for the second an d higher orders. Below the transition region the agreement is rather p oor in low orders, but quite impressive in fourth order. For SU(2) we performed the calculation up to second order. The agreement with the d ata is somewhat worse than in the abelian case.