Quantum Ostrogradsky theorem

Hayato Motohashi (Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan; Division of Liberal Arts, Kogakuin University, 2665-1 Nakano-machi, Hachioji, Tokyo, 192-0015, Japan) ; Teruaki Suyama (Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8551, Japan)

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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      "surname": "Suyama", 
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      "value": "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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Published on:
04 September 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 9
Pages 1-10
DOI:
https://doi.org/10.1007/JHEP09(2020)032
arXiv:
2001.02483
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: