Moment Problems and the Causal Set Approach to Quantum Gravity

Details Moment Problems and the Causal Set Approach to Quantum Gravity Moment Problems and the Causal Set Approach to Quantum Gravity

2002-09-06

arxiv.org/abs/gr-qc/0209020v1

J.Math.Phys. 44 (2003) 1666-1678

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages. To appear: Journal of Mathematical Physics

Scientific paper

10.1063/1.1519668

We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle, and a renormalizability condition. The corresponding dynamics are completely determined by a sequence of nonnegative real coupling constants. Using techniques related to the classical moment problem, we give a complete description of any such sequence of coupling constants. We prove a representation theorem: every discrete theory of quantum gravity arising from causal set dynamics satisfying covariance, causality and renormalizability corresponds to a unique probability distribution function on the nonnegative real numbers, with the coupling constants defining the theory given by the moments of the distribution.

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