Matrix elements of the plaquette operator of Lattice Gauge Theory

In recent papers[1, 2] we proposed a group theoretical description of the Hilbert space for lattice gauge theories (LGT) in the Hamiltonian framework[3]. This approach, based on representation theory, allows to overcome the problem of selecting the gauge invariant Hilbert space. In particular, the difficulty of explicitly solving Mandelstam’s identities[5] in the context of Wilson loops[4] is circumvented. Moreover, such an approach yields a general setting for the computation of the matrix elements of the relevant operators. We will briefly sketch the main concepts underlying our construction and present a physically interesting application as an example.