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A theory for the multipolar excitations in the antiferro-quadrupolar (AFQ) phase of CeB _{6 } is developed. It is based on a pseudo-spin model for the Γ _{8 } ground state of Ce used previously to explain the *B *- *T * phase diagram. An equation of motion method for the multipolar operators is employed and the solutions for the *O *_{2 }^{0 } and *O *_{x y } phases are given. It is shown that the excitation branches are classified as being of mixed quadrupolar-dipolar, quadrupolar-octupolar and octupolar-dipolar character. The former two have strong and the latter only weak dispersion respectively. The transition from the *O *_{2 }^{0 } to the *O *_{x y } phase in the symmetric model is accompanied by the reappearance of a quadrupolar Goldstone mode. In the *O *_{x y } phase of the asymmetric model some modes are gapped already at zero field and for finite field no Goldstone mode remains. In addition we give a derivation for the dynamical structure function based on the mixing scheme of multipolar excitations and discuss the result for the zero-field case.

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