Classical Group Field Theory

Abstract

The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored) defined over a tensor product of the same group, we address the issue of translation and dilatation symmetries and the corresponding Noether theorem. The energy momentum tensor and dilatation current are derived and their properties identified for each case.

References in corpus (16)

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• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Group field theory renormalization - the 3d case: power counting of divergences
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• Diffeomorphisms in group field theories
• EPRL/FK Group Field Theory
• Lost in Translation: Topological Singularities in Group Field Theory
• Phase Transition in Dually Weighted Colored Tensor Models
• Radiative corrections in the Boulatov-Ooguri tensor model: The 2-point function
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
• Generalization of the Bollobás-Riordan polynomial for tensor graphs
• Twisted Hopf symmetries of canonical noncommutative spacetimes and the no-pure-boost principle
• Quantum Mechanics on SO(3) via Non-commutative Dual Variables
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• Ward-Takahashi identities for the colored Boulatov model

Cited by in corpus (4)

• Towards a double-scaling limit for tensor models: probing sub-dominant orders
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• Continuous point symmetries in Group Field Theories