Effective particle kinematics from Quantum Gravity

TL;DR

This paper derives an effective particle kinematics framework in de Sitter spacetime using topological BF theory and Chern-Simons theory, revealing Planck-scale deformations in particle interactions.

Contribution

It introduces a novel approach to particle kinematics in quantum gravity by connecting topological BF theory with boundary Chern-Simons theory and identifying Planck-scale deformation effects.

Findings

Particles exhibit standard kinetic behavior with Planck-scale deformation effects.

Effective theory captures topological interactions at zeroth order perturbation.

Deformation parameter linked to Planck mass influences interaction terms.

Abstract

Particles propagating in de Sitter spacetime can be described by the topological BF $\SO(4,1)$ theory coupled to point charges. Gravitational interaction between them can be introduced by adding to the action a symmetry breaking term, which reduces the local gauge symmetry down to $\SO(3,1)$, and which can be treated as a perturbation. In this paper we focus solely on topological interactions which corresponds to zeroth order in this perturbative expansion. We show that in this approximation the system is effectively described by the $\SO(4,1)$ Chern-Simons theory coupled to particles and living on the 3 dimensional boundary of space-time. Then, using Alekseev--Malkin construction we find the effective theory of particles kinematics. We show that the particles action contains standard kinetic terms and the deformation shows up in the presence of interaction terms. The strength of the interactions is proportional to deformation parameter, identified with Planck mass scale.