Dynamical realizations of the Lifshitz group

@article{Galajinsky2022DynamicalRO,
  title={Dynamical realizations of the Lifshitz group},
  author={Anton V. Galajinsky},
  journal={Physical Review D},
  year={2022}
}
  • A. Galajinsky
  • Published 25 January 2022
  • Mathematics, Physics
  • Physical Review D
Dynamical realizations of the Lifshitz group are studied within the group–theoretic framework. A generalization of the 1 d 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… 

Figures from this paper

The group-theoretic approach to perfect fluid equations with conformal symmetry

The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal

Scalar

. We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (“particles”) of Lie groups generated by spatial rotations, temporal and spatial translations and an additional

Lifshitz symmetry: Lie algebras, spacetimes and particles

. We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (“particles”) of Lie groups generated by spatial rotations, temporal and spatial translations and an additional

References

SHOWING 1-10 OF 24 REFERENCES

Galilean conformal mechanics from nonlinear realizations

We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a nonrelativistic contraction of its

Cosmological aspects of the Eisenhart–Duval lift

A cosmological extension of the Eisenhart–Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed

Dynamical realization of l-conformal Galilei algebra and oscillators

Gravity duals for non-relativistic CFTs

We attempt to generalize the AdS/CFT correspondence to non-relativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity,

Gravity Duals of Lifshitz-Like Fixed Points

We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation

Geometry of conformal mechanics

Conformal mechanics, the simplest conformal field theory, is reformulated as a d=1 nonlinear sigma model on the group SO(1,2). Its action and equation of motion are shown to have a simple

Nonrelativistic conformal groups

In this work a systematic study of finite-dimensional nonrelativistic conformal groups is carried out under two complementary points of view. First, the conformal Killing equation is solved to obtain

Bargmann structures and Newton-Cartan theory.

It is shown that Newton-Cartan theory of gravitation can best be formulated on a five-dimensional extended space-time carrying a Lorentz metric together with a null parallel vector field. The

Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry

We discuss a realization of the nonrelativistic conformal group (the Schr\"odinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field

Celestial mechanics, conformal structures, and gravitational waves.

The problem can be reduced to one with time-independent inverse-square-law forces for a rescaled position vector and a new time variable and the results for a general time-dependent $G(t)$ are also applicable by suitable reinterpretation to the motion of point particles in an expanding universe.