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arXiv · 2001.02483

Quantum Ostrogradsky theorem

Hayato Motohashi·Teruaki Suyama
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Abstract

The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly depends on the canonical momenta. Recently, the original theorem has been generalized to nondegeneracy with respect to non-highest-order derivatives. These theorems have been playing a central role in construction of sensible higher-derivative theories. We explore quantization of such nondegenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.

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Hayato Motohashi, Teruaki Suyama. 2020-01-08. Quantum Ostrogradsky theorem. https://doi.org/10.1007/jhep09(2020)032

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