Quantum model of geometric extension
(1) Computer Center of the Russian Academy of Sciences, Vavilova 40, Moscow 119991 GSP-1, Russia
We construct a model of space-time structure on the basis of the operator field theory. Instead of a world point, the carrier of possible local events is assumed to be a universal supermatrix complex U which comprises a complete set of local field operators. A basic element of extension is described in the model by an equation of a special commutator algebra closed on two such local complexes U1 and U2, "nearest" in the lightlike connection and connected by one vertex of virtual interaction of fields. The corresponding causal relationship is interpreted in the classical picture of the description as a lightlike line closed as a "figure-of-eight" loop, and in the quantum picture as a symmetric T-time jump (reflection) between the nearest local past and future. The discrete nature of the constructed "quantum proximity" equation, containing the gravitational constant, is associated with the existence of a local curvature on the Planck scale. The algebraic closedness of the fundamental equation suggests that the charge symmetry group should be E6 with non-standard representations for fermionic and scalar fields. The model also makes it possible to consider the symmetric two-way time flow as a chain of local T-reflections.
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