Quantum Ostrogradsky theorem

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.

5 pages; added analysis for more general cases; matches published version

References in corpus (2)

• Third order equations of motion and the Ostrogradsky instability
• On the Quantisation of Complex Higher Derivative Theories and Avoiding the Ostrogradsky Ghost

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