Comment on the theory of singletons
نویسنده
چکیده
We study solutions of the equation (△− λ)ω = 0 for even p-forms on the covering space CAdSd of the d-dimensional Anti de-Sitter space and their connection to the unitary irreducible representations of S̃O(d−1, 2). The singleton representation is discussed in detail. Taking into account properly chosen boundary conditions, we find that “singleton modes” are not present among the solutions of the field equations in the bulk of CAdSd. We also obtain solutions of the Flato – Fronsdal singleton dipole equation and show that they do not contain “singleton modes” either. The singleton UIR can, however, be realized on a specially constructed Hilbert space as well as on the space of functions on the boundary of CAdSd. e-mail [email protected]
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