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Gauge-independent analysis of dynamical systems with Chern-Simons term.

Quantization of theories involving the coupling of the Chern-Simons term to complex scalars and Dirac fermions is carried out in the Hamiltonian formalism without using gauge constraints. The covariance under the Poincare group of transformations is established and subtleties in defining the different (canonical or symmetric) forms of the energy-momentum tensor are examined. Gauge-invariant multivalued (anyon) operators obeying graded statistics are found which create the physical states with arbitrary spin. The spin-statistics connection is verified. Implications of our analysis concerning the claimed violation of translation invariance in phenomenological Lagrangians and its connection to anyon superconductivity are also discussed.