Quantum Ostrogradsky theorem
- Resource Type
- Working Paper
- Authors
- Motohashi, Hayato; Suyama, Teruaki
- Source
- JHEP 2020, 32 (2020)
- Subject
- High Energy Physics - Theory
General Relativity and Quantum Cosmology
- Language
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.
Comment: 5 pages; added analysis for more general cases; matches published version