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  Laplacians on discrete and quantum geometries

Calcagni, G., Oriti, D., & Thürigen, J. (2013). Laplacians on discrete and quantum geometries. Classical and quantum gravity, 30(12): 125006. doi:10.1088/0264-9381/30/12/125006.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-E55A-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-156B-7
Genre: Journal Article

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1208.0354 (Preprint), 522KB
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 Creators:
Calcagni, Gianluca1, Author              
Oriti, Daniele1, Author              
Thürigen, Johannes, Author
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: We extend discrete calculus to a bra-ket formalism for arbitrary (p-form) fields on discrete geometries, based on cellular complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its topological dual. The precise implementation of geometric volume factors is not unique and comparing the definition with a circumcentric and a barycentric dual we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries.

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 Dates: 2012-08-0120132013
 Publication Status: Published in print
 Pages: 1+35
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1208.0354
DOI: 10.1088/0264-9381/30/12/125006
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Title: Classical and quantum gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 30 (12) Sequence Number: 125006 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1