Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory
Abstract
We write the SU(2) lattice gauge theory Hamiltonian in (d+1) dimensions in terms of prepotentials which are the SU(2) fundamental doublets of harmonic oscillators. The Hamiltonian in terms of prepotentials has SU(2) U(1) local gauge invariance. In the strong coupling limit, the color confinement in this formulation is due to the U(1) gauge group. We further solve the SU(2) U(1) Gauss law to characterize the physical Hilbert space in terms of a set of gauge invariant integers. We also obtain certain novel gauge invariant operators in terms of the above oscillators. The corresponding prepotential formulation of SU(N) lattice gauge theory is also simple and discussed.
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