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 non-degenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.
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ArXiv ePrint: 2001.02483
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Motohashi, H., Suyama, T. Quantum Ostrogradsky theorem. J. High Energ. Phys. 2020, 32 (2020). https://doi.org/10.1007/JHEP09(2020)032
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DOI: https://doi.org/10.1007/JHEP09(2020)032