A definition of the Ponzano-Regge quantum gravity model in terms of surfaces
نویسنده
چکیده
The Ponzano-Regge quantum gravity model has been a mystery since the time of its construction [1]. Ponzano and Regge found an unexpected relation between the 6j-symbol and Regge’s discrete version of the action functional of (Euclidean) general relativity in 3-dimensions. The description of the relation follows. Consider a 3-dimensional simplex manifold, which consists of tetrahedra whose faces are attached to one another. Pick a tetrahedron and denote the lengths of its edges by ls (s = 1, 2, · · · , 6) such that (l1, l2, l3), (l3, l4, l5), (l1, l5, l6) and (l2, l6, l4) form the four faces of the tetrahedron. (See Fig. 1.) The Regge action for the tetrahedron is
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