Abstract
Totally symmetric arbitrary spin massless and massive free fields in flat and AdS spaces and conformal fields in flat space are studied. Extended gauge invariant hamiltonian action for such fields is obtained. The action is constructed out of phase space fields and Lagrange multipliers which are free of algebraic constraints. Gauge transformations of the phase space fields and Lagrange multipliers are derived. Use of the Poincare parametrization of AdS space allows us to treat fields in flat space and AdS space on equal footing.
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