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

Lattice field computations via recursive numerical integration