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Fields and Laplacians on Quantum Geometries · Around

2013

Fields and Laplacians on Quantum Geometries

Thürigen, Johannes

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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.

Built on

C. Rovelli, Quantum Gravity
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J. Ambjørn, J. Jurkiewicz, and R. Loll, Phys. Rev. Lett
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O. Lauscher and M. Reuter, JHEP
2005
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H.W. Hamber, Quantum Gravitation: The Feynman Path Integral Approach
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Then

D. Oriti, 2012 Foundations of Space and Time: Reflections on Quantum Gravity ed G Ellis et al (Cambridge: Cambridge University Press) [ arXiv:1110.5606 ]
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2012
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