Spinors and Voros star-product for Group Field Theory: First Contact
General Relativity and Quantum Cosmology
2013-05-30 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1107.5693,
title = {Spinors and Voros star-product for Group Field Theory: First Contact},
author = {Maité Dupuis and Florian Girelli and Etera R. Livine},
journal= {arXiv preprint arXiv:1107.5693},
year = {2013}
}
Comments
23 pages