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Nonlinear realizations of the SO(4,2) group are discussed from the point ofview of symmetries. Dynamical symmetry breaking is introduced. One linear andone quadratic model in curvature are constructed. Coherent states of theKlauder-Perelomov type are defined for both cases taking into account the cosetgeometry. A new spontaneous compactification mechanism is defined in thesubspace invariant under the stability subgroup. The physical implications ofthe symmetry rupture in the context of non-linear realizations and directgauging are analyzed and briefly discussed.

Dynamical symmetries, coherent states and nonlinear realizations: the SO(2,4) case