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Stückelberg Fields on the Effective p-brane

We demonstrate the one-to-one correspondence between reparametrization invariant effective actions for relativistic p-branes in flat target space and effective actions for transverse brane perturbations with non-linearly realized Poincaré symmetry. Starting with an action with non-linearly realized symmetry we construct the corresponding reparametrization invariant action by introducing Stückelberg fields. They combine with the transverse modes to form a Lorentz vector. The manifest Lorentz symmetry of the reparametrization invariant action follows directly from the non-linearly realized Lorentz symmetry of the initial action in terms of the physical modes.