Alternative actions for quantum gravity and intrinsic rigidity of space-time

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 grav...

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Bibliographic Details
Published in:Nuclear physics. B 1997-02, Vol.486 (1), p.390-412
Main Authors: Ambjørn, J., Savvidy, G.K., Savvidy, K.G.
Format: Article
Language:English
Subjects:
Integral invariants
Membranes
Rigidity of space-time
Simplicial gravity
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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.
ISSN:0550-3213
1873-1562
DOI:10.1016/S0550-3213(96)00660-8