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 non-relativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension D=d+1 (no central charges), as well as in the special dimension D=2+1 with one "exotic" central charge. We obtain new classical mechanics models which extend the standard (D=0+1) conformal mechanics in the presence of d non-vanishing space dimensions.

Note:

v2: 1 + 20 pages, small changes in Sect.5 and two references added; the version will appear in Phys.Rev.D

11.10.-z
11.25.Hf
11.10.Kk
nonlinear realization
Galilei conformal group
inverse Higgs effect
mechanics: conformal
representation: nonlinear
mechanics: classical
algebra: conformal

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