Abstract
Using the formalism of spherical harmonics, the massless and massive bosonic and fermionic modes on S4 are determined. As on S7, there are extra massless scalar modes, but unlike on S7 there are no scalar modes with negative adS(mass)2, nor any with a conformally invariant field equation. A detailed discussion is given of the conformal symmetries which survive the gauge fixing and which are needed to eliminate spurious scalar modes. Also the diagonalisation of the massive spin-2 and spin-3/2 modes, and of the coupled spin-1 modes, is discussed.
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