First order analytic diagonalization of lattice QCD.

Abstract

The first order plaquette expansion of lattice Hamiltonians is applied to QCD with two massless quarks. Analytic expressions are obtained for the vacuum energy density ${\mathit{scrE}}_{0}$(g) and lowest vector and nucleon masses ${\mathit{M}}_{\mathit{V}}$(g) and ${\mathit{M}}_{\mathit{N}}$(g). The vacuum energy density is valid into the weak coupling region down to about ${\mathit{g}}^{2}$\ensuremath{\sim}0.8, demonstrating the genuine nonperturbative nature of these approximates. The ``specific heat'' derived from ${\mathit{scrE}}_{0}$(g) agrees well with numerical calculations in the t expansion. The ratio R=${\mathit{M}}_{\mathit{N}}$/${\mathit{M}}_{\mathit{V}}$ increases from the strong coupling limit of zero to a more realistic value of R\ensuremath{\sim}1.2\ensuremath{\rightarrow}1.3 at the transition from strong to weak coupling.