Related papers: Remarks on twisted noncommutative quantum field th…
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wave length physics of the system is precisely the supersymmetric nonlinear sigma-model for quasi…
The canonical commutation relations of quantum field theory require all pairs of observables located in spacelike-separated regions to commute. In the theory as it is currently constituted, this implies that the information-carrying…
The paper is devoted to a description of quantum group structures in the geometric quantization of a self-interacting string field, which appear under a transition from a tree-level of the theory to the account of loop effects in…
A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum…
In this paper we study the phenomenon of UV/IR mixing in noncommutative field theories from the point of view of world-sheet open-closed duality in string theory. New infrared divergences in noncommutative field theories arise as a result…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
Using the recent advances in our understanding of non-perturbative aspects of type II strings we show how non-trivial exact results for $N=2$ quantum field theories can be reduced to T-dualities of string theory. This is done by…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Discussion of physical realization of coordinates demonstrates that the quantum theory of gravity (still absent) should be non-local and, probably, non-commutative as well.
Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where…
We construct an effective conformal field theory by using a procedure which induces twisted boundary conditions for the fundamental scalar fields. That allows to describe a quantum Hall fluid at Jain hierarchical filling, nu=m/(2pm+1), in…
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no…
We study the possibility of obtaining noncommutative gravity dynamics from string theory in the Seiberg-Witten limit. We find that the resulting low-energy theory contains more interaction terms than those proposed in noncommutative…
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…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…