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Abstract: (World Scientific)
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.Note:
- 3 pages, submitted to the Proceedings of the 13th Marcel Grossmann Meeting (MG13), Stockholm, July 1-7, 2012
- Lattice methods
- Loop quantum gravity
- quantum geometry
- spin foams
- geometry: discrete
- quantum gravity: loop space
- dimension: spectral
- field theory: group
- quantum geometry
- Regge calculus
References(14)
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