Measure of the path integral in lattice gauge theory

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U(1) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.