On state sums, internalisation and unification

Details On state sums, internalisation and unification On state sums, internalisation and unification

2004-04-29

arxiv.org/abs/gr-qc/0404121v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

This paper has been withdrawn by the author due to its speculative nature

Scientific paper

In this mostly expository article, elements of higher category theory essential to the construction of a class of four dimensional quantum geometric models are reviewed. These models improve current state sum models for Quantum Gravity, such as the Barrett-Crane model, in that they appear, for instance, to remove degeneracies which swamp the partition function. Much work remains to be done before a complete construction is reached, but the crucial categorical notion of internalisation already illuminates the idea that a full unified model may result from few, albeit as yet poorly understood, additional principles. In particular, a spacetime and matter duality principle is employed through an understanding of the role of pseudomonoidal objects in categorified cohomology.

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