De Sitter Gauge Theory Research Articles

Indefinite harmonic forms and gauge theory

Indecomposable representations have been extensively used in the construction of conformal and de Sitter gauge theories. It is thus noteworthy that certain unitary highest weight representations have been given a geometric realization as the unitary quotient of an indecomposable representation using indefinite harmonic forms [RSW]. We apply this construction toSU (2,2) and the de Sitter group. The relation is established between these representations and the massless, positive energy representations ofSU (2,2) obtained in the physics literature. We investigate the extent to which this construction allows twistors to be viewed as a gauge theory ofSU (2,2). For the de Sitter group, on which the gauge theory of singletons is based, we find that this construction is not directly applicable.

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincare-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.

Poincaré and de Sitter gauge theories of gravity with propagating torsion

We consider a gauge approach to the gravitational theory based on the local Poincar\'e ${P}_{10}$ or de Sitter ${S}_{10}$ groups. The ${P}_{10}$ gauge rotations and translations take place in the tangent spaces to the space-time manifold. We interpret the independence of matter fields from the tangent vectors as the necessity to use a nonlinear realization of the ${P}_{10}$ or ${S}_{10}$ groups thus effectively breaking the full symmetry to the Lorentz group. The Lagrangian we choose is the ${S}_{10}$ Yang-Mills invariant with the space-time metric expressed in terms of the translational part of the ${S}_{10}$ nonlinear gauge field. Various consequences of the theory are discussed, including the correspondence with general relativity, the propagating spin-connection interactions, the analogy with the chiral Higgs mechanism, instantonlike solutions, a possibility of gravitational repulsion due to the noncompactness of the Lorentz group, etc. We also analyze the quantization of the theories with torsion with special emphasis on the presence of the nonlinear realization. We stress the possibility of obtaining a renormalizable theory if the metric is not quantized but is expressed in terms of a mean value of the quantized ${S}_{10}$ nonlinear gauge field.

General relativity as a limit of the de Sitter gauge theory

The gauge character of the vierbein field is investigated by introducing the Yang-Mills fields associated with the de Sitter gauge group and by contracting the de Sitter group to the Poincar\'e group. The vierbein field can indeed be seen as a gauge field consisting of the Yang-Mills fields associated with both the Lorentz and the translational symmetry. The local Lorentz invariance is found essential to deduce Einstein's theory of general relativity.