Abstract
We present an alternative method for constructing a consistent perturbative low energy canonical formalism for higher-order time-derivative theories, which consists in applying the standard Dirac method to the first-order version of the higher-order Lagrangian, augmented by additional perturbative Hamiltonian constraints. The method is purely algebraic, provides the dynamical formulation directly in phase space and can be used in singular theories without the need of initially fixing the gauge. We apply it to two paradigmatic examples: the Pais–Uhlenbeck oscillator and the Bernard–Duncan scalar field with self-interaction. We also compare the results, both at the classical and quantum level, with the ones corresponding to a direct perturbative construction applied to the exact higher-order theory, after incorporating the projection to the space of physical modes. This comparison highlights the soundness of the present formalism.
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