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Ostrogradsky's theorem on Hamiltonian instability
Open accessAbstract
Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian field theories. A discussion is given of the problems raised by attempts to evade this restriction.
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Cited by
Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
Langlois, D., & Noui, K. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/02/034 · Cited by 653
Teleparallel gravity: from theory to cosmology
Bahamonde, S., Dialektopoulos, K. F., Escamilla-Rivera, C., Farrugia, G., Gakis, V., Hendry, M., Hohmann, M., Levi Said, J., Mifsud, J., & Di Valentino, E. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac9cef · Cited by 503
Dark Energy Versus Modified Gravity
Joyce, A., Lombriser, L., & Schmidt, F. (2016) · Annual Review of Nuclear and Particle Science · doi:10.1146/annurev-nucl-102115-044553 · Cited by 463
A systematic approach to generalisations of General Relativity and their cosmological implications
Heisenberg, L. (2019) · Physics Reports · doi:10.1016/j.physrep.2018.11.006 · Cited by 419
“As can clearly be seen, the equations of motion are at most second order in the derivatives, avoiding the Ostrogradski instability [94, 95].”
BackgroundDegenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
Ben Achour, J., Langlois, D., & Noui, K. (2016) · Physical Review D · doi:10.1103/physrevd.93.124005 · Cited by 331
Metadata
- Authors
- Woodard, R.
- Venue
- Scholarpedia
- Publisher
- Scholarpedia
- Published
- 2015
- Volume
- 10
- Issue
- 8
- Pages
- 32243
- ISSN
- 1941-6016 (ISSN-L)
- OpenAlex
- W1261499239
- Cited by
- 552
- References
- 0
- FWCI
- 21.99
- Type
- journal article
- Language
- en
- Open access
- diamond
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