  We investigate the application of efficient recursive numerical integration
strategies to models in lattice gauge theory from quantum field theory. Given
the coupling structure of the physics problems and the group structure within
lattice cubature rules for numerical integration, we show how to approach these
problems efficiently by means of Fast Fourier Transform techniques. In
particular, we consider applications to the quantum mechanical rotor and
compact U(1) lattice gauge theory, where the physical dimensions are two and
three. This proceedings article reviews our results presented in J. Comput.
Phys 443 (2021) 110527.
