Fields and Laplacians on Quantum Geometries

Thürigen, Johannes

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Fields and Laplacians on Quantum Geometries

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Thürigen, Johannes
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1302.7135
(Preprint), 112KB

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Thürigen, J. (2015). Fields and Laplacians on Quantum Geometries. In The Thirteenth Marcel Grossmann Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories - Proceedings of the MG13 Meeting on General Relativity (pp. 2168-2170). World Scientific Publishing.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-EB42-4

Abstract

In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows.