Encoding simplicial quantum geometry in group field theories

Abstract

We show that a new symmetry requirement on the GFT field, in the context of an extended GFT formalism, involving both Lie algebra and group elements, leads, in 3d, to Feynman amplitudes with a simplicial path integral form based on the Regge action, to a proper relation between the discrete connection and the triad vectors appearing in it, and to a much more satisfactory and transparent encoding of simplicial geometry already at the level of the GFT action.

15 pages, 2 figures, RevTeX, references added

References in corpus (8)

• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Path integral representation of spin foam models of 4d gravity
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Spin foam model from canonical quantization
• A Lagrangian approach to the Barrett-Crane spin foam model
• Causality and matter propagation in 3d spin foam quantum gravity
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• A Note on B-observables in Ponzano-Regge 3d Quantum Gravity

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• On the geometry of loop quantum gravity on a graph
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Non-commutative flux representation for loop quantum gravity
• Lost in Translation: Topological Singularities in Group Field Theory
• Spinfoams in the holomorphic representation
• Bubbles and jackets: new scaling bounds in topological group field theories
• A Deformed Poincare Invariance for Group Field Theories