Non-commutative quantum geometric data in group field theories

Abstract

We review briefly the motivations for introducing additional group-theoretic data in tensor models, leading to the richer framework of group field theories, themselves a field theory formulation of loop quantum gravity. We discuss how these data give to the GFT amplitudes the structure of lattice gauge theories and simplicial gravity path integrals, and make their quantum geometry manifest. We focus in particular on the non-commutative flux/algebra representation of these models.

10 pages; to appear in the proceedings of the workshop "Non-commutative field theory and gravity", Corfu', Greece, EU, September 2013

References in corpus (3)

• Group field theory with non-commutative metric variables
• The Tensor Track, III
• Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data

Cited by in corpus (2)

• Group field theory for quantum gravity minimally coupled to a scalar field
• Inequivalent coherent state representations in group field theory