Group field theory with non-commutative metric variables

Abstract

We introduce a dual formulation of group field theories, making them a type of non-commutative field theories. In this formulation, the variables of the field are Lie algebra variables with a clear interpretation in terms of simplicial geometry. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. This formulation suggests ways to impose the simplicity constraints involved in BF formulations of 4d gravity directly at the level of the group field theory action. We illustrate this by giving a new GFT definition of the Barrett-Crane model.

4 pages; v3 published version

References in corpus (6)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• Group field theory renormalization - the 3d case: power counting of divergences
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• A Lagrangian approach to the Barrett-Crane spin foam model

Cited by in corpus (9)

• EPRL/FK Group Field Theory
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• Spinfoams in the holomorphic representation
• Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• Quantum Mechanics on SO(3) via Non-commutative Dual Variables
• Two-point functions in (loop) quantum cosmology
• Gravity as an emergent phenomenon: a GFT perspective
• On the depth of quantum space