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Abstract: It is well known that in a generally covariant gravitational theory thechoice of spacetime scalars as coordinates yields phase-space observables or-invariants-. However their relation to the symmetry group of diffeomorphismtransformations has remained obscure. In a symmetry-inspired approach weconstruct invariants out of canonically induced active gauge transformations.These invariants may be intepreted as the full set of dynamical variablesevaluated in the intrinsic coordinate system. The functional invariants canexplicitly be written as a Taylor expansion in the coordinates of any observer,and the coefficients have a physical and geometrical interpretation.Surprisingly, all invariants can be obtained as limits of a family of canonicaltransformations. This permits a short again geometric proof that allinvariants, including the lapse and shift, satisfy Poisson brackets that areequal to the invariants of their corresponding Dirac brackets.



Author: J. M. Pons, D. C. Salisbury, K. A. Sundermeyer

Source: https://arxiv.org/







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