Abstract
We argue that the obstacles to having a first-order formalism for odd-derivative actions presented in a pedagogical note by Deser (Class. Quantum Grav. 23 5773) are based on examples which are not first-order forms of the original actions. The general derivation of an equivalent first-order form of the original second-order action is illustrated using the example of topologically massive electrodynamics (TME). The correct first-order formulations of the TME model keep intact the gauge invariance presented in its second-order form demonstrating that the gauge invariance present in the original action is not lost when one correctly employs the Ostrogradsky procedure.
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