| A new model of elementary particles based on the geometry of "Quantum deSitter space" QdS = SU(3,2)/{dollar}{lcub}{dollar}SU(3,1) {dollar}times{dollar} U(1){dollar}{rcub}{dollar} is introduced and studied. QdS is a complexification or "quantization" of "anti-de Sitter space", AdS = SO(3,2)/SO(3,1), which in recent years has played a pivotal role in supergravity. The nontrival principle fiber bundle has total space SU(3,2), fiber SU(3,1) {dollar}times{dollar} U(1) and base QdS. In this setting, the standard recipes for Yang-Mills fields don't work. These require connections and the associated covariant derivatives. Here it is shown that the Lie derivatives, not the covariant derivatives are important in quantization. In this setting, the no-go theorems are not valid. This new quantum mechanics leads to a model of elementary particles as vertical vector fields in the bundle with interaction via the Lie bracket. There are five physical interactions modelled by the bracket interaction. The quantum numbers are identified as the roots of su(3,2) and are preserved under the bracket interaction. The model explains conservation of charge, baryon number, lepton number, parity and the heirarchy problem. Since the bracket is the curvature of a homogeneous space, particles are then the curvature of QdS. This model for particles is consistent with the requirements of General Relativity. Furthermore, since the curvature tensor is built from the quantized wave functions, the curvature tensor is quantized and this is quantum theory of gravity. |
