Simplicial gravity with coordinates
نویسندگان
چکیده
We present a formulation of Regge Calculus where arbitrary coordinates are associated to each vertex simplicial complex and the degrees freedom given by metric on simplex. The lengths edges thus determined left invariant under transformations discrete set coordinates, provided transforms accordingly. Invariance coordinate entails tensor calculus our follows closely usual formalism continuum theory. definitions parallel transport, Christoffel symbol, covariant derivatives Riemann curvature follow in rather natural way. In this correspondence Einstein action becomes with deficit angle $\theta$ replaced $\sin \theta$. theory can be extended actions higher powers tensor, vielbein coupling gravity matter fields (scalars, fermionic including spin $3/2$ gauge fields) which then unambiguously discussed paper. An lattice for $N=1$ supergravity $4$ dimensions is derived context. Another relavant result that Yang-mills consist, even absence gravity, two plaquettes terms, unlike one plaquette Wilson hypercubic lattice. attempt also made formulate differential include forms order gauging free algebras scheme. However leads form products do not satisfy associativity distributive law respect $d$ operator. A proper theories contain context still lacking.
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ژورنال
عنوان ژورنال: Classical and Quantum Gravity
سال: 2021
ISSN: ['1361-6382', '0264-9381']
DOI: https://doi.org/10.1088/1361-6382/abf66d