Regge calculus: applications to classical and quantum gravity
Regge calculus is a simplicial approximation to general relativity which preserves many topological and geometrical properties of the exact theory. After discussing the foundations of this technique and deriving some basic identities, specific solutions to Regge calculus are analyzed. In particular, the flat Friedmann-Robertson-Walker (FRW) model is shown. This particular model is used in the discussion of the initial value problem for Regge calculus. An Arnowitt-Deser-Misner type of 3 + 1 decomposition is possible only under very special circumstances; solutions with a non-spatially constant lapse can not generally be decomposed. The flat FRW model is also used to compute the accuracy of this approximation method developed by Regge. A three-dimensional toy model of quantum gravity is discussed that was originally formulated by Ponzano and Regge. A more thorough calculation is performed that takes into account additional terms. The renormalization properties of this model are shown. Finally, speculations are made on the interaction of the geometry, topology and quantum effects using Regge calculus, which, because of its simplicial nature, makes these effects more amenable to calculation and intuition.
- Research Organization:
- Maryland Univ., College Park (USA)
- OSTI ID:
- 5794922
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
GEOMETRY
GRAVITATION
MATHEMATICAL MODELS
MATHEMATICS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
REGGE CALCULUS
RENORMALIZATION
TOPOLOGY