Prepotential formulation of SU(3) lattice gauge theory

Understand

The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential harmonic oscillators.

• This reformulation has enlarged $SU(3)\otimes U(1) \otimes U(1)$ gauge invariance under which the prepotential operators transform like matter fields.
• The Hilbert space of SU(3) lattice gauge theory is shown to be equivalent to the Hilbert space of the prepotential formulation satisfying certain color invariant Sp(2,R) constraints.
• The SU(3) irreducible prepotential operators which solve these Sp(2,R) constraints are used to construct SU(3) gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge invariant vertex operators.