Generating Functions for Lattice Gauge Models with Scaled Fermions and Bosons

Recently, employing an imaginary-time functional integral formulation, we considered abelian and nonabelian (aZ)d lattice quantum field gauge theories with new a-dependent locally scaled Wilson Fermi and Bose fields in d4 spacetime dimensions and neglecting the pure gauge interaction. The use of scaled fermions and bosons preserves Osterwalder-Schrader positivity and the spectral content of the models since the decay rates of correlations in the infinite-time limit are unchanged. In addition, scaled fields also result in a less singular, more regular behavior in the continuum limit. The scaled field gauge models are thermodynamically stable, which shows that stability does not depend on the presence of a pure gauge, plaquette term in the action. The finite lattice free energy is bounded with a bound independent of the number of points of the lattice and the lattice spacing a(0,1]. Recall that the expansion of the fermionic exponential bond factor, arising from the interacting nearest neighbor hopping terms in the action, is finite by Pauli exclusion. The Bose-Gauge models we consider here have a finite truncation of the bond factor; the Fermi-mimicking truncated Bose models still obey Osterwalder-Schrader positivity. We show boundedness of the n-point scaled field generating functions and n-point scaled field correlations. The bounds are independent of the number of lattice points and the lattice spacing a(0,1]. For the truncated Bose models, the bound is also independent of the location of the n points. No renormalization of the parameters is needed. The precise a-dependent factors have been extracted and isolated from the unscaled field partition functions and correlations so that the scaled field free energies and correlations are not singular for a(0,1].