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Moment Problems and the Causal Set Approach to Quantum Gravity

Avner Ash·Patrick McDonald
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Abstract

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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Avner Ash, Patrick McDonald. 2002-09-06. Moment Problems and the Causal Set Approach to Quantum Gravity. https://doi.org/10.1063/1.1519668

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