**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Wednesday, June 29, 2022 — 10:00 AM EDT

Bob Room at Perimeter Institute and Zoom (please email amgrad@uwaterloo.ca for the Zoom meeting link)

Qiaoyin Pan | Applied Mathematics, University of Waterloo

*q*-deformed LQG in three-dimensional space-time

Loop quantum gravity (LQG) is a canonical, background-independent and non-perturbative approach to quantum gravity. This thesis is devoted to studying three-dimensional (3D) quantum gravity with a non-vanishing cosmological constant Λ in the LQG approach. In particular, we focus on the case of Λ negative in the Euclidean signature where the isometry group is SL(2, *C*). We construct the *q-deformed LQG model* with the real deformation parameter *q *encoding the value of *|*Λ|. In this model, the kinematical and physical Hilbert spaces of gravity exhibit the quantum group symmetries consistent with other approaches to 3D quantum gravity. The LQG model with Λ =0 is recovered at *q**→*1. This quantum gravity model is derived from the classical theory using the standard canonical quantization program *à la* Dirac and the mathematical connection between quantum groups and Lie bialgebras. We establish this model first in terms of the holonomy-flux algebra and then in terms of spinors, which are purely geometrical objects. We write the quantum Hamiltonian constraint with spinors and recover the Turaev-Viro amplitudes defined in the spinfoam model, which is a covariant approach to quantum gravity written in a discrete path integral formalism. We also use spinors to reconstruct the spinfoam model in a way that the local building blocks to construct global 3D geometry are conformal. This is done for the Λ =0 case as a first step. The *q*-deformed LQG model is topological and describes the curved geometries in 3D as well as on 2D spatial surfaces. It is expected to serve as a better starting point to connect LQG with other quantum gravity approaches and generalize to 4D LQG with a non-vanishing Λ.

Event tags

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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