Symmetry reduction of spatiotemporal zeta functions via space-group quotienting

Develop a symmetry-reduced formulation of the spatiotemporal zeta function that quotients all spacetime and internal symmetries for hypercubic lattice field theories, generalizing the one-dimensional dihedral space-group treatment to higher-dimensional crystallographic space groups.

Background

The current presentation utilizes only the translation subgroup, while full space-group and internal symmetries can lead to redundancy in counting and to improved convergence when properly quotiented.

A symmetry-reduced zeta function analogous to Lind’s topological zeta or the dihedral-space group zeta in one dimension would likely sharpen analytic properties and computational efficiency in higher dimensions.