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- Higher Symmetry of Gravity and the Cosmological Constant Problem

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08060091

According to Doering and Isham the spectral topos corresponds to any quantum system. The descriptions of the systems become similar to these given by classical theories. Topoi can also modify local smooth spacetime structure. Supposing that a quantum system modifies the local spacetime structure and interacts with a gravitational field via the spectral topos, a natural pattern for non-gravitating quantum zero-point modes of the system, appears. A way how to add gravity into the spectral topos of a system is presented. A theory of gravity and systems should be symmetric with respect to some 2-group derived from the category of systems. Hence, a fundamental symmetry of gravity is rather 2-group of automorphisms of the category of systems. This higher symmetry is responsible for the vanishing of the cotributions to the cosmological constant derived from zero-point modes of energy of quantum systems in spacetime. A connection with strings (via the coefficients of the 2-connection of some 2-bundle, with this 2group as the structure group) is also shown. Institute of Physics, University of Silesia

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