ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Scalar functions on the homogeneous spaces HR of the de Sitter group G=SO(4,1) are studied, where the spaces HR are of the form G/K with K being a subgroup of the Lorentz group H=SO(3,1) contained in SO(4,1). The spaces HR can be regarded as fiber bundles ER=ER(G/H,H/K), with the base V′4 =G/H being a space of constant negative curvature characterized by a fundamental length parameter R[(4,1)-de Sitter space], and the fiber S=H/K being a homogeneous space of the Lorentz group. The action of G on the spaces ER is a linear action on V4 and a nonlinear action on S, where the latter action is defined by a generalized Wigner rotation. A gauge theory based on the (4,1)-de Sitter group is investigated with matter represented in terms of a generalized wave function Φ(x;ξ,y˜) [with x∈U4 (Riemann–Cartan space-time), ξ∈V′4, and y˜∈S] which is defined as a map from a cross section on the bundle E=E(U4, F=ER, G=SO(4,1)) over space-time U4 with fiber F=ER =G/K and structural group G=SO(4,1) into the complex numbers. The introduction of purely nonlinearly transforming fields (N)Φ(x;y˜) is discussed as well as the nonlinear realization of the SO(4,1) symmetry in terms of transformations of the Lorentz subgroup H (generalized Wigner rotations). The geometric implications of symmetry breaking are pointed out.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.526796
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