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.
{ "_oai": { "updated": "2021-01-25T22:46:38Z", "id": "oai:repo.scoap3.org:56786", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Japan", "value": "Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan", "organization": "Kyoto University" }, { "country": "Japan", "value": "Division of Liberal Arts, Kogakuin University, 2665-1 Nakano-machi, Hachioji, Tokyo, 192-0015, Japan", "organization": "Kogakuin University" } ], "surname": "Motohashi", "email": "motohashi@cc.kogakuin.ac.jp", "full_name": "Motohashi, Hayato", "given_names": "Hayato" }, { "affiliations": [ { "country": "Japan", "value": "Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8551, Japan", "organization": "Tokyo Institute of Technology" } ], "surname": "Suyama", "email": "suyama@tap.scphys.kyoto-u.ac.jp", "full_name": "Suyama, Teruaki", "given_names": "Teruaki" } ], "titles": [ { "source": "Springer", "title": "Quantum Ostrogradsky theorem" } ], "dois": [ { "value": "10.1007/JHEP09(2020)032" } ], "publication_info": [ { "page_end": "10", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2020", "artid": "JHEP09(2020)032", "year": 2020, "page_start": "1", "journal_issue": "9" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2020-12-25T01:31:00.407180", "source": "Springer", "method": "Springer", "submission_number": "5299df22464811ebbd0e02163e01809a" }, "page_nr": [ 10 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2020" } ], "control_number": "56786", "record_creation_date": "2020-09-05T05:30:18.148940", "_files": [ { "checksum": "md5:7301320b33e1372b5504606d7d1153d4", "filetype": "xml", "bucket": "ddcc5913-2662-4569-be4c-1823fbe50536", "version_id": "3c14a34f-5f20-43d6-8ddc-d555b2ba1e00", "key": "10.1007/JHEP09(2020)032.xml", "size": 11277 }, { "checksum": "md5:a9a13841afce7e94a523a28b39cee56d", "filetype": "pdf/a", "bucket": "ddcc5913-2662-4569-be4c-1823fbe50536", "version_id": "a30c1c08-d1cc-4358-9948-811a65688fa4", "key": "10.1007/JHEP09(2020)032_a.pdf", "size": 219709 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "gr-qc" ], "value": "2001.02483" } ], "abstracts": [ { "source": "Springer", "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." } ], "imprints": [ { "date": "2020-09-04", "publisher": "Springer" } ] }