2016/12/20 by V. M. Khatsymovsky, Khatsymovsky, V. M.
Physics and Astronomy · #53C05 #83C27 #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #msc:53C05 #msc:83C27
paper · pdf · doi:10.48550/arxiv.1612.06727
6 pages, report given at the International conference "Quantum Field Theory and Gravity 2016", August 1-7, 2016, TSPU, Tomsk, Russia
arxiv created 2016/12/20 · arxiv updated 2016/12/21
The gravity action on the piecewise flat Riemannian manifold is formulated using the discrete set of the nondegenerate 4×4 matrices on the 3-simplices as some connection type variables. These variables are the discrete counterpart of the affine (Christoffel) connection used as independent variables in the Palatini form of the Einstein gravity action. Excluding these with the help of the equations of motion we get the original discrete gravity action on the piecewise flat spacetime (Regge action). The discrete version of the diffeomorphisms and path integral are briefly discussed.