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I read the following statement in Wald's book and it is a bit unclear to me.

"The isometry group of spacetime acts in a natural way on the states of a physical system."

  1. In what sense the isometry group of spacetime acts on states?

  2. Does it mean that the isometry group of spacetime is the same as the symmetry group of a physical system?

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  • $\begingroup$ The same Lie group. $\endgroup$ – Cinaed Simson Nov 19 at 7:25

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