$1$-Loop Theory

Abstract

A new formalism for lattice gauge theory is developed that preserves Poincaré symmetry in a discrete universe. We define the $1$-loop, a generalization of the Wilson loop that reformulates classical differential equations of motion as identity-valued multiplicative loops of Lie group elements of the form $[g_1\cdots g_n]=1$. A lattice Poincaré gauge theory of gravity is thus derived that employs a novel matter field construction and recovers Einstein's vacuum equations in the appropriate limit.

10 pages, 3 figures