On the perturbative expansion of a quantum field theory around a topological sector

Carlo Rovelli (1, 2) , Simone Speziale (3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]

The idea of treating general relativistic theories in a perturbative expansion around a topological theory has been recently put forward in the quantum gravity literature. Here we investigate the viability of this idea, by applying it to conventional Yang--Mills theory on flat spacetime. We find that the expansion around the topological theory coincides with the usual expansion around the abelian theory, though the equivalence is non-trivial. In this context, the technique appears therefore to be viable, but not to bring particularly new insights. Some implications for gravity are discussed.

Mots clés: quantum gravity; loop quantum gravity; topological theories

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Carlo Rovelli, Simone Speziale. On the perturbative expansion of a quantum field theory around a topological sector. General Relativity and Gravitation, 2007, 39 (2), pp.167-178. ⟨hal-00008394⟩