Clifford Algebras, Multipartite Systems and Gauge Theory Gravity

TL;DR

This paper develops a multipartite gauge theory gravity framework using space-time algebra, linking it to quantum information, black hole physics, and the standard model, revealing algebraic structures and entanglement properties.

Contribution

It introduces a novel multipartite formulation of gauge theory gravity using geometric algebra, connecting it to quantum information and particle physics.

Findings

Algebraic Hopf-like structure emerges from the formalism.

Entangled qubits are derived from minimal left ideals.

Applications to black holes and the standard model are outlined.

Abstract

In this paper we present a multipartite formulation of gauge theory gravity based on the formalism of space-time algebra for gravitation developed by Lasenby and Doran (Lasenby, A. N., Doran, C. J. L, and Gull, S.F.: Gravity, gauge theories and geometric algebra. Phil. Trans. R. Soc. Lond. A, 582, 356:487 (1998)). We associate the gauge fields with description of fermionic and bosonic states using the generalized graded tensor product. Einstein's equations are deduced from the graded projections and an algebraic Hopf-like structure naturally emerges from formalism. A connection with the theory of the quantum information is performed through the minimal left ideals and entangled qubits are derived. In addition applications to black holes physics and standard model are outlined.