Alternative actions for quantum gravity and intrinsic rigidity of space-time. (English) Zbl 0925.83010
Summary: We generalize the Regge action of simplicial quantum gravity by ascribing deficit angles to the vertices of four-dimensional simplicial manifolds. The new terms suppress vertices with deficit angles different from zero and introduce in this way so-called intrinsic rigidity in simplicial quantum gravity. The concept of generalized deficit angles appear in a natural way in the Steiner-Weyl expansion formula for parallel manifolds and is related to higher order curvature terms. We discuss the concept of rigidity in quantum gravity and its relation to the so-called goni-hedric principle. This principle allows us to find a large class of integral invariants defined on simplicial manifolds of various dimensions. These invariants are natural candidates for discretized actions for higher dimensional membranes.
MSC:
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
| 83C45 | Quantization of the gravitational field |
Keywords:
Regge action; Steiner-Weyl expansion formula; parallel manifolds; integral invariants; string model extensionsReferences:
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