Related papers: Noncommutative Geometry and the Standard Model: An…
In this note the noncommutative geometry is interpreted as a functor, whose range is a family of the operator algebras. Some examples are given and a program is sketched.
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
Massive neutrinos can be accommodated into the noncommutative geometry reinterpretation of the Standard Model. The constrained Standard Model Lagrangian is computed anew under the assumption of nonzero neutrino masses. This gives the…
The triumphs of the Standard Model of Particle Physics call attention upon an old idea, that the so-called vacuum is an accessible physical medium, and not just a tautology. I take this idea as a serious working hypothesis, and I suggest a…
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The…
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…
I briefly review the conceptual developments that led to the Standard Model and discuss some of its remarkable qualitative features. On the way, I draw attention to several puzzling aspects that are beyond the reach of our present…
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…
This is a compilation of some well known propositions of Alain Connes concerning the use of noncommutative geometry in mathematical physics.
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
We study varieties defined over nonstandard fields using techniques of nonstandard mathematics.
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes…
The popular generalized additive model framework is extended to allow both the mean curves and the response distribution to be nonparametric. The approach is demonstrated to be a flexible yet parsimonious tool for data analysis in its own…
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
We investigate the effect of the noncommutative geometry on the classical orbits of particles in a central force potential. The relation is implemented through the modified commutation relations $[x_i, x_j]=i \theta_{ij} $. Comparison with…
We introduce a notion of the noncommutative integrability within a framework of contact geometry.
We discuss the renormalization properties of noncommutative non-gauge supersymmetric field theories.