Spinors and Voros star-product for Group Field Theory: First Contact

Understand

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.