2018/11/17 by V. M. Khatsymovsky, Khatsymovsky, V. M.
Physics and Astronomy · #53C05 #83C27 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.1811.07160
openalex publication_date 2018/11/17 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
Faddeev gravity using a d-dimensional tetrad (normally d = 10) is\nclassically equivalent to general relativity (GR).\n The discrete Faddeev gravity on the piecewise flat spacetime normally assumes\nslowly varying metric and tetrad from vertex to vertex. Meanwhile, Faddeev\naction is finite (although not unambiguously defined) for discontinuous tetrad\nfields thus allowing, in particular, to consider a surface as consisting of\nvirtually independent elementary triangles, and its area spectrum as the sum of\nelementary area spectra. In the discrete connection form, area tensors are\ncanonically conjugate to SO(10) connection matrices, and earlier we have found\nthe elementary area spectrum, which is nonsingular just at large connection or\nthe strongly varying fields constituting a kind of "antiferromagnetic"\nstructure.\n We appropriately define discrete it connection Faddeev action to\nunambiguously determine the discrete Faddeev action for the strongly varying\nfields, but weakly varying metric, equivalent in the continuum limit to the GR\naction with this metric. Previously, we considered large variations in only one\ndirection, now we use an ansatz in some respects less common, but overall,\nprobably the most common.\n A unified simplicial connection representation is written out (depending on\nan auxiliary connection) both for the discrete Faddeev action and for the Regge\naction.\n