Classical and quantum stability of higher-derivative dynamics
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the ti...
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| Veröffentlicht in: | The European physical journal. C, Particles and fields Particles and fields, 2014-10, Vol.74 (10), p.1-19, Article 3072 |
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| container_title | The European physical journal. C, Particles and fields |
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| creator | Kaparulin, D. S. Lyakhovich, S. L. Sharapov, A. A. |
| description | We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the time-translation invariance. A procedure is suggested for switching on interactions in free higher-derivative systems without breaking their stability. We also demonstrate the quantization technique that keeps the higher-derivative dynamics stable at quantum level. The general construction is illustrated by the examples of the Pais–Uhlenbeck oscillator, higher-derivative scalar field model, and the Podolsky electrodynamics. For all these models, the positive integrals of motion are explicitly constructed and the interactions are included such that they keep the system stable. |
| doi_str_mv | 10.1140/epjc/s10052-014-3072-3 |
| format | Article |
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C</stitle><date>2014-10-01</date><risdate>2014</risdate><volume>74</volume><issue>10</issue><spage>1</spage><epage>19</epage><pages>1-19</pages><artnum>3072</artnum><issn>1434-6044</issn><eissn>1434-6052</eissn><abstract>We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the time-translation invariance. A procedure is suggested for switching on interactions in free higher-derivative systems without breaking their stability. We also demonstrate the quantization technique that keeps the higher-derivative dynamics stable at quantum level. The general construction is illustrated by the examples of the Pais–Uhlenbeck oscillator, higher-derivative scalar field model, and the Podolsky electrodynamics. 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| subjects | Astronomy Astrophysics and Cosmology Construction Dynamical systems Dynamics Electrodynamics Elementary Particles Hadrons Heavy Ions Integrals Measurement Science and Instrumentation Nuclear Energy Nuclear Physics Oscillators Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Regular Article - Theoretical Physics Scalars Stability String Theory |
| title | Classical and quantum stability of higher-derivative dynamics |
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