The U(1)₃ Lattice Gauge Vacuum

Abstract

We adapt the method of correlated basis functions for a semi-analytic ab-initio treatment of lattice gauge models in the Hamiltonian formulation. The vacuum ground state of the quantum electrodynamic U(1)₃ model on a square lattice is described by a Jastrow trial function and is optimized by employing the minimum principle of the ground state energy. We construct the associated optimal elementary excitations in the uncharged sector by setting up an appropriate Feynman eigenvalue equation. Numerical calculations on this set of states and associated quantities at coupling parameters 0 ≤ λ ≤ 6 are performed in conjunction with the hypernetted-chain approximation. Numerical results are presented on optimized single-plaquette quantities such as the plaquette energy, the single-plaquette profile and the mean-field potential. We report further on pair-plaquette quantities such as the electric and magnetic field correlation functions which depend not only on the strength parameter A but also on the relative plaquette distance. We present numerical data on the energies of the lowest branch of elementary excitations and, particularly, on the optimized lattice-photon (glueball) mass. The results are discussed and compared with previous numerical results and future improvements are indicated. We finally demonstrate the stability of the vacuum ground state with respect to the local fluctuations represented by the optimal elementary excitations.