论文标题
Lifshitz组的动态实现
Dynamical realizations of the Lifshitz group
论文作者
论文摘要
在组理论框架内研究了Lifshitz组的动态实现。构建了1D共形力学的概括，涉及任意动力学指数z。提出了类似的Ermakov-Milne-Pinney方程的概括。引入了不变的导数和现场组合，这使人们能够构建享受Lifshitz对称性的众多动力系统。构建了（D+2）二维时空和能量弹药张量的Lorentzian签名度量，这导致了施加爱因斯坦方程的广义Ermakov-Milne-Pinney方程。非线性实现的方法用于使用Lifshitres等轴测组构建Lorentzian指标。特别是，构建了（2D+2）维度度量，在加利利（Galilei）的提升下具有额外的不变性。
Dynamical realizations of the Lifshitz group are studied within the group-theoretic framework. A generalization of the 1d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z. A similar generalization of the Ermakov-Milne-Pinney equation is proposed. Invariant derivative and field combinations are introduced, which enable one to construct a plethora of dynamical systems enjoying the Lifshitz symmetry. A metric of the Lorentzian signature in (d+2)-dimensional spacetime and the energy-momentum tensor are constructed, which lead to the generalized Ermakov-Milne-Pinney equation upon imposing the Einstein equations. The method of nonlinear realizations is used for building Lorentzian metrics with the Lifshitz isometry group. In particular, a (2d+2)-dimensional metric is constructed, which enjoys an extra invariance under the Galilei boosts.
