Integral-spin fields on (3+2)-de Sitter space

Journal Article · Thu Dec 01 04:00:00 EST 1988 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.528094· OSTI ID:6751374

Gazeau, J; Hans, M

Nowadays, (3+2)-de Sitter (or anti-de Sitter space) appears as a very attractive possibility at several levels of theoretical physics. The Wigner definition of an elementary system as associated to a unitary irreducible representation of the Poincare group may be extended to the de Sitter group SO(3,2) (or approx.(SO(3,2))) without great difficulty. The constant curvature, as small as it can be, is a natural candidate to play the role of a regularization parameter with respect to the flat-space limit. Massless particles in (3+2)-de Sitter theory are composite (singletons). On the other hand, supergravity theories necessitate a (large) constant curvature. The content of this paper is group theoretical. It attempts to continue the ''a la Wigner'' program for SO(3,2), already largely broached by Fronsdal. Three recurrence formulas are presented. They permit one to build up the carrier states for representations with arbitrary integral spin. Two of them are valid for the ''massive'' representations whereas the third one is applicable to the indecomposable massless representations. In addition, other presumably indecomposable, though nonphysical, representations are studied, in relation to the existence of ''generalized'' gauge fields and divergences. The recurrence formulas also allow one to build up the invariant two-point functions or homogeneous propagators.

• Research Organization: Laboratoire de Physique Theorique et Mathematique, Universite Paris 7, Equipe de Recherches Centre National de la Recherche Scientifique 177, 2, place Jussieu, 75251 Paris Cedex 05, France
• OSTI ID: 6751374
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 29:12; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
CASIMIR OPERATORS
COSMOLOGICAL MODELS
DE SITTER GROUP
FIELD THEORIES
GENERAL RELATIVITY THEORY
GROUP THEORY
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
LIGHT CONE
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
PARTICLE PROPERTIES
POINCARE GROUPS
QUANTUM FIELD THEORY
RECURSION RELATIONS
RELATIVITY THEORY
RENORMALIZATION
SCALAR FIELDS
SO GROUPS
SPACE-TIME
SPIN
SYMMETRY GROUPS