The scalar potential in noncommutative geometry

The Scalar Potential in Noncommutative Geometry

We present a derivation of the general form of the scalar potential in Yang-Mills theory of a non-commutative space which is a product of a four-dimensional manifold times a discrete set of points. We show that a non-trivial potential without flat directions is obtained after eliminating the auxiliary fields only if constraints are imposed on the mass matrices utilised in the Dirac operator. Th...

Singlet scalar dark matter in noncommutative space

In this paper, we examine the singlet scalar dark matter annihilation to becoming the Standard Model particles in the non-commutative space. In the recent decades, many candidates of dark matter have been offered,  but our information about  the nature of dark matter is still limited. There are such particle candidates as  scalar matetr, fermion, boson, gauge boson, etc.; however, they have nei...

New Scalar Fields in Noncommutative Geometry

In this publication we present an extension of the Standard Model within the framework of Connes’ noncommutative geometry [1]. The model presented here is based on a minimal spectral triple [7] which contains the Standard Model particles, new vectorlike fermions and a new U(1) gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new ferm...

Coulomb Potential of a Point Mass in Theta Noncommutative Geometry

Abstract. We investigate the form of the Coulomb potential of a point charge in a noncommutative geometry, using a state of minimal dispersion. We find the deviation of the potential at large distances from the point, distinguishing between coordinate distance and measured distance. Defining the “effective” value of an operator as its expectation value in a minimum dispersion state centered at ...

Noncommutative geometry