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We argue that the field-parametrization dependence of Dirac's procedure, forHamiltonians with first-class constraints not only preserves covariance incovariant theories, but in non-covariant gauge theories it allows one to findthe natural field parametrization in which the Hamiltonian formulationautomatically leads to the simplest gauge symmetry.

Field-parametrization dependence of Dirac's method for constrained  Hamiltonians with first-class constraints: failure or triumph? Non-covariant  models