Spinors and Voros star-product for Group Field Theory: First Contact
arXiv:1107.5693 · doi:10.1103/PhysRevD.86.105034
Abstract
In the context of non-commutative geometries, we develop a group Fourier transform for the Lie group SU(2). Our method is based on the Schwinger representation of the Lie algebra su(2) in terms of spinors. It allows us to prove that the non-commutative R^3 space dual to the SU(2) group is in fact of the Moyal-type and endowed with the Voros star-product when expressed in the spinor variables. Finally, from the perspective of quantum gravity, we discuss the application of these new tools to group field theories for spinfoam models and their interpretation as non-commutative field theories with quantum-deformed symmetries.
23 pages
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- Spinors and Twistors in Loop Gravity and Spin Foams
- Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
- On the space of generalized fluxes for loop quantum gravity
- Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
- Weighting bubbles in group field theory
- Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
- 3D Quantum Gravity from Holomorphic Blocks
- Aspects of Group Field Theory