Summary
We study the algebra of the Poisson brackets, of the constraints in the ADM formulation of general relativity and we derive it from the gauge algebra. We discuss the gauge transformations in the canonical framework and we obtain a direct geometrical interpretation of the constraint algebra. In the same way the constraint commutator algebra is derived from the gauge algebra in the quantum theory.
Riassunto
Si studia l'algebra delle parentesi di Poisson dei vincoli, nella formulazione ADM della relatività generale e la si deriva dall'algebra di gauge. Si discutono le trasformazioni di gauge nell'ambito della teoria canonica e si ottiene un'interpretazione geometrica diretta dell'algebra dei vincoli. Analogamente l'algebra dei commutatori dei vincoli è derivata dall'algebra di gauge nella teoria quantistica.
Резюме
Мы исследуем алгебру скобок Пуассона для ограничений в ADM формулировке общей теории относительности. Мы выводим эту алгебру из калибровочной алгебры. Мы обсуждаем калибровочные преобразования в рамках канонического подхода. Мы получаем непосредственнуй интерпретацию алгебры ограничений. Аналогично выводится алгебра коммутаторов из калибровочной алгебры в квантовой теории.
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Rovelli, C. Constraint algebra in general relativity. Nuov Cim B 92, 49–60 (1986). https://doi.org/10.1007/BF02729696
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DOI: https://doi.org/10.1007/BF02729696