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Algebraic structures in quantum gravity
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DOI：10.1088/0264-9381/27/9/095008.png)
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Abstract
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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.
Keywords:
DYSON-SCHWINGER EQUATIONS
HOPF-ALGEBRAS
FIELD-THEORY
RENORMALIZATION
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