Density matrix and dynamical aspects of Quantum Mechanics with Fundamental Length

Abstract

In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix deformation. The corresponding deformed density matrix, which is called density pro-matrix is given explicitly. It properties have been investigated as well as some dynamical aspects of the theory. In particular, the deformation of Liouville equation is analyzed in detail. It was shown that Liouville equation in Quantum Mechanics appears as a low energy limit of deformed Liouville equation in Quantum Mechanics with Fundamental Length. Some implications of obtained results are presented as well as their application to the calculation of black hole entropy.

arXiv comment14 pages, Latex,some corrections of the section 2

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• Non-Unitary and Unitary Transitions in Generalized Quantum Mechanics and Information Problem Solving
• Deformed Quantum Field Theory, Thermodynamics at Low and High Energies, and Gravity. I
• Some Implications of the Density Matrix Deformation in Statistical Mechanics of the Early Universe
• The Quantum and Statistical Theory of Early Universe and Its Possible Applications to Cosmology