Explicit Hamiltonian for SU(2) lattice gauge theory

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Abstract
We study pure SU(2) gauge theory in the Hamiltonian formulation in 2+1 and 3+1 dimensions. We treat both the vacuum sector and the sector having two static color charges. These two sectors are required for calculations of glueballs and string tension. All gauge arbitrariness is eliminated, and we formulate the Hamiltonian in terms of variables that are gauge invariant except for freedom under a single global SU(2) transformation. The Hamiltonian is given explicitly as a differential operator in the parameters for these essentially gauge-invariant variables. We discuss practical applications of the Hamiltonian.