Dynamical realizations of the Lifshitz group

Abstract

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.

v3: presentation in sect. 2 and sect. 5 improved, one reference added; the version accepted for publication in Phys. Rev. D

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Cited by in corpus (2)

• Lifshitz symmetry: Lie algebras, spacetimes and particles
• The group-theoretic approach to perfect fluid equations with conformal symmetry