2011

Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model

Baratin, Aristide, Oriti, Daniele

Understand

A dual formulation of group field theories, obtained by a Fourier transform mapping functions on a group to functions on its Lie algebra, has been proposed recently.

  • In the case of the Ooguri model for SO(4) BF theory, the variables of the dual field variables are thus so(4) bivectors, which have a direct interpretation as the discrete B variables.
  • Here we study a modification of the model by means of a constraint operator implementing the simplicity of the bivectors, in such a way that projected fields describe metric tetrahedra.
  • This involves a extension of the usual GFT framework, where boundary operators are labelled by projected spin network states.

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