Affiliation:
1. Budker Institute of Nuclear Physics of Siberian Branch Russian Academy of Sciences, Novosibirsk 630090, Russia
Abstract
The piecewise flat space–time is equipped with a set of edge lengths and vertex coordinates. This defines a piecewise affine coordinate system and a piecewise affine metric in it, the discrete analogue of the unique torsion-free metric-compatible affine connection or of the Levi-Civita connection (or of the standard expression of the Christoffel symbols in terms of metric) mentioned in the literature, and, substituting this into the affine connection form of the Regge action of our previous work, we get a second-order form of the action. This can be expanded over metric variations from simplex to simplex. For a particular periodic simplicial structure and coordinates of the vertices, the leading order over metric variations is found to coincide with a certain finite difference form of the Hilbert–Einstein action.
Publisher
World Scientific Pub Co Pte Lt
Subject
Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics
Cited by
6 articles.
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