Dynamical realizations of l-conformal Newton-Hooke group

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• 作者：Anton Galajinsky ; ^{galajin@tpu.ru} ; Ivan Masterov ^{masterov@tpu.ru}
• 关键词：Conformal Newton&ndash ; Hooke algebra ; Dynamical realizations ; Pais&ndash ; Uhlenbeck oscillator
• 刊名：Physics Letters B
• 出版年：2013
• 出版时间：10 June, 2013
• 年：2013
• 卷：723
• 期：1-3
• 页码：190-195
• 全文大小：226 K

文摘

The method of nonlinear realizations and the technique previously developed in [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212, ] are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A configuration space of the model involves coordinates, which parametrize a particle moving in d spatial dimensions and a conformal mode, which gives rise to an effective external field. The dynamical system describes a generalized multi-dimensional oscillator, which undergoes accelerated/decelerated motion in an ellipse in accord with evolution of the conformal mode. Higher derivative formulations are discussed as well. It is demonstrated that the multi-dimensional Pais-Uhlenbeck oscillator enjoys the -conformal Newton-Hooke symmetry for a particular choice of its frequencies.