Algebraic structures in quantum gravity

Details Algebraic structures in quantum gravity Algebraic structures in quantum gravity

2009-09-30

arxiv.org/abs/0909.5631v2

Class.Quant.Grav.27:095008,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, 5 figues, relation with group field theory investigated; version accepted for publication in Class. Quant. Grav

Scientific paper

10.1088/0264-9381/27/9/095008

Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with quantum field theory, from a combinatorial point of view. A grafting operator is introduced allowing for the equivalent of a Dyson-Schwinger equation to be written. Non-trivial examples are explicitly worked out. Finally, the physical significance of the results is discussed.

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