Dynamical realizations of the Lifshitz group
Abstract
Dynamical realizations of the Lifshitz group are studied within the grouptheoretic framework. A generalization of the 1 d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z . A similar generalization of the ErmakovMilnePinney 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 energymomentum tensor are constructed, which lead to the generalized ErmakovMilnePinney 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 (2 d +2 )dimensional metric is constructed, which enjoys an extra invariance under the Galilei boosts.
 Publication:

Physical Review D
 Pub Date:
 May 2022
 DOI:
 10.1103/PhysRevD.105.106023
 arXiv:
 arXiv:2201.10187
 Bibcode:
 2022PhRvD.105j6023G
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 v3: presentation in sect. 2 and sect. 5 improved, one reference added