Algebraic structures in quantum gravity

Abstract

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.

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

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Cited by in corpus (10)

• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
• Combinatorial Hopf algebra for the Ben Geloun-Rivasseau tensor field theory
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• Some combinatorial aspects of quantum field theory
• Translation-Invariant Noncommutative Renormalization
• Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach
• A word Hopf algebra based on the selection/quotient principle
• A selection-quotient process for packed word Hopf algebra
• Renormalization group-like proof of the universality of the Tutte polynomial for matroids
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory