Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

摘要: Relying on known results of the Noether theory symmetries extended to constrained systems, it is shown that there exists an obstruction prevents certain tangent-space diffeomorphisms be projectable phase-space, for generally covariant theories. This main result throws new light old fact algebra gauge generators in phase space General Relativity, or other theories, only closes as a soft and not Lie algebra. The deep relationship between these two issues clarified. In particular, we see second one may understood side effect procedure solve first. It explicitly how adoption specific metric-dependent diffeomorphisms, way achieve projectability, causes (constraints) --with structure constants-- but {\it functions}.