Eisenhart lift for higher derivative systems

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• 作者：Anton Galajinsky ; ^{galajin@tpu.ru} ; Ivan Masterov ^{masterov@tpu.ru}
• 关键词：Higher derivative mechanics ; Eisenhart lift
• 刊名：Physics Letters B
• 出版年：2017
• 出版时间：10 February 2017
• 年：2017
• 卷：765
• 期：Complete
• 页码：86-90
• 全文大小：266 K
• 卷排序：765

文摘

The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric. In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian. A consistent geometric description seems feasible only for a particular class of potentials. The scheme is exemplified by the Pais–Uhlenbeck oscillator.