相关论文: The emergence of Noncommutative Potential Theory
The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
Modifications in the energy momentum dispersion laws due to a noncommutative geometry, have been considered in recent years. We examine the oscillations of extended objects in this perspective and find that there is now a "generation" of…
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
A purely imaginary potential can provide a phenomenological description of creation and absorption of quantum mechanical particles. PT-invariance of such a potential ensures that the non-unitary phenomena occur in a balanced manner. In…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into…
We complete our previous recent review on noncommutative field theory, discussing in particular the constructive aproach to the Grosse-Wulkenhaar theory. We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy…
These lecture notes were written during a mini-course on noncommutative Lp-spaces at the Basque Center of Applied Mathematics. It starts presenting the theory of weights and traces in von Neumann algebra, followed by the theory of…
Density matrix perturbation theory [Phys. Rev. Lett. Vol. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of response properties [Phys. Rev. Lett. Vol. 92, 193002 (2004)]. In this article, we generalize…
Implications of noncommutative field theories with commutator of the coordinates of the form $[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu \nu}x^{\omega}$with nilpotent structure constants are investigated. It is shown that a free…
We establish the ultra-violet finiteness of various classes of noncommutative gauge theories.
We study the properties of the energy-momentum tensor in non-commutative gauge theories by coupling them to a weak external gravitational field. In particular, we show that the stress tensor of such a theory coincides exactly with that…
Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the…
A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie…
Due to the lack of the translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize the energy band theory to the…
We study the quantum backflow problem in the noncommutative plane. In particular, we have considered a charged particle with and without an oscillator interaction with noncommuting momentum operators and examined angular momentum backflow…
We show that the algebra of functions on noncommutative space allows two different representations. One is describing the genuine noncommutative space, while another one can be rewritten in commutative form by a redefinition of generators.