Origin of q-deformation in Loop quantum gravity with cosmological constant - Julian Rennert

The spin network states of Loop quantum gravity with vanishing cosmological constant are constructed from representations of the Lie group SU(2). Motivated by the combinatorial quantization of Chern-Simons theory, it is believed that a non-zero cosmological constant leads to q-deformed spin networks, which are built from certain representations of a quantum group.

We will detail in this talk how we can understand the origin of this q-deformation from the perspective of Loop quantum gravity. We focus on 3d gravity with a positive cosmological constant and its quasi-Poisson structure on the classical side as well as the corresponding quasi-Hopf structures in the quantum theory. Finally, we will discuss the relevance of our findings to other spacetime signatures, dimensions and values of the cosmological constant.

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Thursday, November 1, 2018 - 14:30 to 16:00
Location: 
Space Room
Room #: 
400