Numerical Methods in LQG
SUMMER2019
Lectures at the 2019 Bard Summer School on Quantum Gravity - None
In this lecture, I discuss generic numerical calculations in Loop Quantum Gravity. In the first part, we examine spin networks, the kinematical states of Loop Quantum gravity. We derive and numerically compute the spectrum of geometric observables (areas, angles, and volumes). In the second part, we introduce coherent states peaked on intrinsic geometry. We analyze numerically the reasons for the geometric interpretation as convex polyhedra. In the last part, we give hints of spinfoam calculations, focussing on the Ponzano-Regge model.
Course materials:
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Mathematica notebook with some preliminary material.
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Mathematica notebook with spin networks calculations.
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Mathematica notebook with coherent states calculations.
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Mathematica notebook with spin foams calculations with the Ponzano-Regge model.
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Original paper on the Ponzano-Regge model 'Semiclassical limit of Racah Coefficients' (1968). It is difficult to find online. If you have a cleaner version feel free to contact me.
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Paper origami to visualize how curvature is encoded in a discrete model.