Related papers: Non-anti-commutative deformation of complex geomet…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Connes' noncommutative approach to the standard model of electromagnetic, weak and strong forces is sketched as well as its unification with general relativity.
We study the conditions under which N=(1,1) generalized sigma models support an extension to N=(2,2). The enhanced supersymmetry is related to the target space complex geometry. Concentrating on a simple situation, related to Poisson sigma…
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted co-product. This allows for the definition of conformal symmetry in a non-commutative background geometry. The twisted co-product is reviewed for the…
Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant…
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
We define ''convergence'' for noncommutative power series and construct two topologies on the algebra of power series, convergent with respect to a positive radius. We indicate all finite dimensional continuous representations of this…
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in…
In this paper, we present and classify the supersymmetric extensions of extended kinematical algebras, at the basis of non-Lorentzian physics theories. The diverse kinematical superalgebras are here derived by applying non- and…
The supersymmetric extensions of the Schr\"odinger algebra are reviewed.
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.
We study the superspace formulation of the noncommutative nonlinear supersymmetric O(N) invariant sigma-model in 2+1 dimensions. We prove that the model is renormalizable to all orders of 1/N and explicitly verify that the model is…
A lot of developments made during the last years show that Kac-Moody algebras play an important role in the algebraic structure of some supergravity theories. These algebras would generate infinite-dimensional symmetry groups. The possible…
We discuss the renormalization properties of noncommutative supersymmetric theories. We also discuss how the gauge field plays a role similar to gravity in noncommutative theories.
Simultaneous nonlinear realizations of spontaneously broken supersymmetry in conjunction with other spontaneous and/or explicitly broken symmetries including R symmetry, global chiral symmetry, dilatations and the superconformal symmetries…
We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. This way symmetry…
The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.
We consider non(anti)commutative superspace with coordinate dependent deformation parameters $C^{\alpha\beta}$. We show that a chiral ${\cal N}=1/2$ supersymmetry can be defined and that chiral and antichiral superfields are still closed…
Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…