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arXiv · 2007.05968

$\mathbb{1}$-Loop Theory

Alexander S. Glasser·Hong Qin
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Abstract

A new formalism for lattice gauge theory is developed that preserves Poincar\'e symmetry in a discrete universe. We define the $\mathbb{1}$-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 ${[g_1\cdots g_n]=\mathbb{1}}$. A lattice Poincar\'e gauge theory of gravity is thus derived that employs a novel matter field construction and recovers Einstein's vacuum equations in the appropriate limit.

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Alexander S. Glasser, Hong Qin. 2020-07-12. $\mathbb{1}$-Loop Theory. https://arxiv.org/abs/2007.05968

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