Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory

Details Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory

2004-03-30

arxiv.org/abs/hep-lat/0403029v1

J.Phys. A38 (2005) 10015-10026

Physics

High Energy Physics

High Energy Physics - Lattice

8 pages, LaTex, no figures

Scientific paper

10.1088/0305-4470/38/46/008

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 $SU(2) \otimes U(1)$ 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 $SU(2) \otimes U(1)$ 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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