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Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries
Author(s) -
Bombelli L.,
Corichi A.,
Winkler O.
Publication year - 2005
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200410144
Subject(s) - transversal (combinatorics) , semiclassical physics , dirac (video compression format) , equations of motion , transformation (genetics) , electromagnetic field , plane wave , physics , plane (geometry) , field (mathematics) , charge (physics) , motion (physics) , quantum , classical mechanics , two body dirac equations , mathematical physics , klein–gordon equation , dirac algebra , dirac equation , quantum mechanics , mathematics , mathematical analysis , geometry , pure mathematics , nonlinear system , biochemistry , chemistry , neutrino , gene
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at “quantum scales” and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a “semiclassical” state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity.