Discrete approaches to quantum gravity in four dimensions. (English) Zbl 1023.83011

Loll, Renate

Living Rev. Relativ. 1, Article No. 1998-13, 35 p. (1998).

Summary: The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. Here the author reviews three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation; quantum Regge calculus; and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.

MSC:

83C45	Quantization of the gravitational field
81V17	Gravitational interaction in quantum theory
83-02	Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
81T13	Yang-Mills and other gauge theories in quantum field theory
81-02	Research exposition (monographs, survey articles) pertaining to quantum theory

Keywords:

discretization of space-time and the Einstein action; gauge-theoretic approaches; path-integral; Hamiltonian formulation; quantum Regge calculus; dynamical triangulations

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