Relativistic spin networks and quantum gravity
John W. Barrett, Louis Crane
TL;DR
This paper introduces relativistic spin networks based on the group SO(4) to model 4-dimensional quantum gravity, extending previous 3D models and proposing a new state sum framework.
Contribution
It defines relativistic spin networks using the spin covering of SO(4) and suggests a 4D state sum model for quantum gravity based on these networks.
Findings
Relativistic spin networks relate to the geometry of 2D faces of a 4-simplex.
Extension of Ponzano-Regge model to 4D using relativistic spins.
Proposal of a new 4D quantum gravity state sum model.
Abstract
Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geometry of the edges of a 3-simplex. This leads us to suggest that there may be a 4-dimensional state sum model for quantum gravity based on relativistic spin networks which parallels the construction of 3-dimensional quantum gravity from ordinary spin networks.
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