Cho-Duan-Ge decomposition Clairaut equation Einstein field equation Hamilton-Jacobi equation Hilbert space linearization Kirchhoff's integral theorem Klein-Gordon-Fock equation Lie-Poisson action Lie-Poisson structure Maxwell's vacuum equations Noether symmetry Physics Poisson manifold Research & information: general abstracting algebra of symmetry operators arithmetic arity asymptotic conditions black holes canonical gravity coherent states conformable differential constraintless formalism covariance current Lie algebra representation current algebra symmetry detector clicks diffeomorphism group dirac reduction