Snorre Harald Christiansen, Tore Gunnar Halvorsen
We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.
Snorre Harald Christiansen, Tore Gunnar Halvorsen
We introduce a numerical method, based on finite elements and lattice gauge theory, to compute approximate solutions to Schrödinger and Pauli equations. The crucial geometric property of the method is discrete gauge invariance. The main new achievement is second order convergence. This is proved by interpreting the method as defined on gauge potential dependent finite element spaces and providing an analysis of such spaces in terms of gauge potential dependent norms on simplices of all dimensions.