Search results for "NONCOMMUTATIVE GEOMETRY"

Elementary symmetric functions of two solvents of a quadratic matrix equations

2008

Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.

Possible extensions of the noncommutative integral

2011

In this paper we will discuss the problem of extending a trace σ defined on a dense von Neumann subalgebra \(\mathfrak{M}\) of a topological *-algebra \({\mathfrak{A}}\) to some subspaces of \({\mathfrak{A}}\). In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra.

Path Integrals in Noncommutative Geometry

2006

Can (noncommutative) geometry accommodate leptoquarks?

1997

We investigate the geometric interpretation of the Standard Model based on noncommutative geometry. Neglecting the $S_0$-reality symmetry one may introduce leptoquarks into the model. We give a detailed discussion of the consequences (both for the Connes-Lott and the spectral action) and compare the results with physical bounds. Our result is that in either case one contradicts the experimental results.

The expansion $\star$ mod $\bar{o}(\hbar^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization

2019

The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these allow generating the Kontsevich graphs, expanding the noncommutative & x22c6;-product by using a priori undetermined coefficients, and deriving linear relations between the weights of graphs. Throughout this text we illustrate the assembly of the Kontsevich & x22c6;-product up to order 4 in the deformation parameter Already at this stage, the & x22c6;-product involves hundreds of graphs; expressing all their coefficients via 149 w…

The su(2|1) Model of Electroweak Interactions and Its Connection to NC Geometry

2002

I review the su(2|1) model of electroweak interactions which is essentially based on the super Lie algebra su(2|1), thus incorporating both usual gauge fields and Higgs fields in one generalized Yang-Mills field. Special emphasis is put on the natural appearance of spontaneous symmetry breaking and other appealing features of the model like generation mixing. Also the connection of the model to noncommutative geometry is briefly discussed.