SPACE, TIME AND FUNDAMENTAL INTERACTIONS

Isospectral symmetries in two-dimensional models with Moyal product

Yurov A.V., Obnoskina A.V., Trunin A.S.

We discuss the Bekenstein constraint and the behavior of entropy in the vicinity of a Big Rip singularity. The horizon size collapses to zero as we approach the singularity and the number of admissible states tends to zero. The situation changes dramatically in the case of quantum fluctuations in non-commutative space-time, which naturally arises in some brane models within the unified M-theory. We describe the mathematical properties of the Moyal multiplication and a non-commutative generalization of the Laplace operator. We show that field models of non-commutative geometry in two-dimensional Lorentzian space admit two types of isospectral discrete symmetries.