Global InformationOstrogradsky instability information
In applied mathematics, the Ostrogradsky instability is a feature of some solutions of theories having equations of motion with more than two time derivatives (higher-derivative theories). It is suggested by a theorem of Mikhail Ostrogradsky in classical mechanics according to which a non-degenerate Lagrangian dependent on time derivatives higher than the first corresponds to a Hamiltonian unbounded from below. As usual, the Hamiltonian is associated with the Lagrangian via a Legendre transform. The Ostrogradsky instability has been proposed as an explanation as to why no differential equations of higher order than two appear to describe physical phenomena.[1] However, Ostrogradsky's theorem does not imply that all solutions of higher-derivative theories are unstable as many counterexamples are known.[2][3][4][5][6][7][8][9][10]
- ^ Motohashi, Hayato; Suyama, Teruaki (2015). "Third-order equations of motion and the Ostrogradsky instability". Physical Review D. 91 (8): 085009. arXiv:1411.3721. Bibcode:2015PhRvD..91h5009M. doi:10.1103/PhysRevD.91.085009. S2CID 118565011.
- ^ Pais, A.; Uhlenbeck, G. E. (1950). "On Field theories with nonlocalized action". Physical Review. 79 (145): 145–165. Bibcode:1950PhRv...79..145P. doi:10.1103/PhysRev.79.145. S2CID 123644136.
- ^ Pagani, E.; Tecchiolli, G.; Zerbini, S. (1987). "On the Problem of Stability for Higher Order Derivatives: Lagrangian Systems". Letters in Mathematical Physics. 14 (311): 311–319. Bibcode:1987LMaPh..14..311P. doi:10.1007/BF00402140. S2CID 120866609.
- ^ Smilga, A. V. (2005). "Benign vs. Malicious ghosts in higher-derivative theories". Nuclear Physics B. 706 (598): 598–614. arXiv:hep-th/0407231. Bibcode:2005NuPhB.706..598S. doi:10.1016/j.nuclphysb.2004.10.037. S2CID 2058604.
- ^ Pavsic, M. (2013). "Stable Self-Interacting Pais-Uhlenbeck Oscillator". Modern Physics Letters A. 28 (1350165). arXiv:1302.5257. Bibcode:2013MPLA...2850165P. doi:10.1142/S0217732313501654.
- ^ Kaparulin, D. S.; Lyakhovich, S. L.; Sharapov, A. A. (2014). "Classical and quantum stability of higher-derivative dynamics". The European Physical Journal C. 74 (3072): 3072. arXiv:1407.8481. Bibcode:2014EPJC...74.3072K. doi:10.1140/epjc/s10052-014-3072-3. S2CID 54059979.
- ^ Pavsic, M. (2016). "Pais-Uhlenbeck oscillator and negative energies". International Journal of Geometric Methods in Modern Physics. 13 (1630015): 1630015–1630517. arXiv:1607.06589. Bibcode:2016IJGMM..1330015P. doi:10.1142/S0219887816300154.
- ^ Smilga, A. V. (2017). "Classical and quantum dynamics of higher-derivative systems". International Journal of Modern Physics A. 32 (1730025). arXiv:1710.11538. Bibcode:2017IJMPA..3230025S. doi:10.1142/S0217751X17300253. S2CID 119435244.
- ^ Salvio, A. (2018). "Quadratic Gravity". Frontiers in Physics. 6 (77): 77. arXiv:1804.09944. Bibcode:2018FrP.....6...77S. doi:10.3389/fphy.2018.00077.
- ^ Salvio, A. (2019). "Metastability in Quadratic Gravity". Physical Review D. 99 (10): 103507. arXiv:1902.09557. Bibcode:2019PhRvD..99j3507S. doi:10.1103/PhysRevD.99.103507. S2CID 102354306.