Poincare group spin networks

Abstract

Spin network technique is usually generalized to relativistic case by changing $SO(4)$ group -- Euclidean counterpart of the Lorentz group -- to its universal spin covering $SU(2)\times SU(2)$, or by using the representations of $SO(3,1)$ Lorentz group. We extend this approach by using inhomogeneous Lorentz group $\mathcal{P}=SO(3,1)⋊{\mathbb{R}}^4$, which results in the simplification of the spin network technique. The labels on the network graph corresponding to the subgroup of translations ${\mathbb{R}}^4$ make the intertwiners into the products of $SU(2)$ parts and the energy-momentum conservation delta functions. This maps relativistic spin networks to usual Feynman diagrams for the matter fields.

RevTex, 7 pages

References in corpus (10)

• Spin Networks and Quantum Gravity
• Relativistic spin networks and quantum gravity
• Spin Foam Models
• ``Sum over Surfaces'' form of Loop Quantum Gravity
• A Lorentzian Signature Model for Quantum General Relativity
• The physical hamiltonian in nonperturbative quantum gravity
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Gravitational edge modes: From Kac-Moody charges to Poincaré networks
• Hidden Quantum Gravity in 3d Feynman diagrams
• Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams

Cited by in corpus (2)

• Combinatorial Spacetime from Loop Quantum Gravity
• A Loop Quantum Gravity Inspired Action for the Bosonic String and Emergent Dimensions at Large Scales