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Loop equations in the theory of gravity

N.A. Voronov, Yuri Makeenko

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Abstract

Loop-space variables (the parallel transport matrices) are considered for the theory of gravity. Loop equations which are equivalent to the Einstein equations are derived in the classical case. Loop equations are also obtained for the case of gravity with a cosmological term. An analogy with the loop-space approach to Yang-Mills theory is discussed.

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What this paper is about

Loop-space variables (the parallel transport matrices) are considered for the theory of gravity. Loop equations which are equivalent to the Einstein equations are derived in the classical case. Loop equations are also obtained for the case of gravity with a cosmological term. An analogy with the loop-space approach to Yang-Mills theory is discussed.

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Available abstract

Loop-space variables (the parallel transport matrices) are considered for the theory of gravity. Loop equations which are equivalent to the Einstein equations are derived in the classical case. Loop equations are also obtained for the case of gravity with a cosmological term. An analogy with the loop-space approach to Yang-Mills theory is discussed.

Key concepts: Loop (graph theory), Analogy, Einstein, Space (punctuation), Physics, Gravitation, Friedmann equations, Mathematics

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