# Four-dimensional spinfoam quantum gravity with a cosmological constant: Finiteness and semiclassical limit

@article{Han2021FourdimensionalSQ, title={Four-dimensional spinfoam quantum gravity with a cosmological constant: Finiteness and semiclassical limit}, author={Muxin Han}, journal={Physical Review D}, year={2021} }

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,C) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4…

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## References

SHOWING 1-10 OF 58 REFERENCES

Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory

- Physics, Mathematics
- 2017

The simplicity constraint is studied in the context of 4d spinfoam models with cosmological constant. We find that the quantum simplicity constraint is realized as the 2d surface defect in…

Divergences in spinfoam quantum gravity

- Physics
- 2012

In this thesis we study the flat model, the main buidling block for the spinfoam approach to quantum gravity, with an emphasis on its divergences. Besides a personal introduction to the problem of…

Cosmological deformation of Lorentzian spin foam models

- Physics
- 2003

We study the quantum deformation of the Barrett?Crane Lorentzian spin foam model which is conjectured to be the discretization of the Lorentzian Plebanski model with positive cosmological constant…

Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory

- Physics
- 2014

Preface Part I. Foundations: 1. Spacetime as a quantum object 2. Physics without time 3. Gravity 4. Classical discretization Part II. The 3D Theory: 5. 3D Euclidean theory 6. Bubbles and cosmological…

4-dimensional Spin-foam Model with Quantum Lorentz Group

- Physics, Mathematics
- 2010

We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model…

New spinfoam vertex for quantum gravity

- Physics
- 2007

We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the…

Four-dimensional quantum gravity with a cosmological constant from three-dimensional holomorphic blocks

- Physics, Mathematics
- 2016

Abstract Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL ( 2 , C ) Chern–Simons…

Quantum deformation of two four-dimensional spin foam models

- Physics, Materials Science
- 2011

We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The q-deformed models are based on the representation theory of…

Lorentzian spin foam amplitudes: graphical calculus and asymptotics

- Physics, Mathematics
- 2010

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude…

Quantization of Chern-Simons gauge theory with complex gauge group

- Mathematics
- 1991

The canonical quantization of Chern-Simons gauge theory in 2+1 dimensions is generalized from the case in which the gauge group is a compact Lie groupG to the case in which the gauge group is a…