A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory

Abstract: We present a tensor formulation for free compact electrodynamics in three Euclidean dimensions and use this formulation to construct a quantum Hamiltonian in the continuous-time limit. Gauge-invariance is maintained at every step and the resulting Hamiltonian can be written as a rotor model. The energy eigenvalues for this Hamiltonian are computed using the tensor formulation, and compared with perturbation theory. We find good agreement between the calculations demonstrating a smooth passage from the statistical lattice Lagrangian description to the quantum Hamiltonian description.