منابع مشابه
Non-commutative Algebraic Geometry
0 Introduction This is a reasonably faithful account of the ve lectures I delivered at the summer course \Geometria Algebraica no Commutativa y Espacios Cuanti-cos" for graduate students, in Spain, July 25{29, 1994. The material covered was, for the most part, an abridged version of Artin and Zhang's paper 2]. Fix a eld k. Given a Z-graded k-algebra, A say, which for simplicity is assumed to be...
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A kinetics built upon q-calculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the “quasi-position” whose eigenvalues are the levels of the hierarchy, corresponding to the volume of phase space available to the system at any given time. Motion along the lattice of quasi-positions is irreversible....
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The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quater-nion) form. It was shown that the plane electromagnetic wave is the solution of the system of non-linear wave equations of the second order for the electric and magnetic induction fields. We have found the...
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We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gr...
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By “parallelogram geometry” we mean the elementary, “commutative”, geometry corresponding to vector addition, and by “trapezoid geometry” a certain “noncommutative deformation” of the former. This text presents an elementary approach via exercises using dynamical software, hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, ...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1993
ISSN: 0033-068X,1347-4081
DOI: 10.1143/ptp/90.1.219