The Fundamental Group of a Noncommutative Space

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...

Noncommutative Regime of Fundamental Physics

We further develop a model unifying general relativity with quantum mechanics proposed in our earlier papers (J. Math. Phys. 38, 5840 (1998); 41, 5168 (2000)). The model is based on a noncommutative algebra A defined on a groupoid Γ = E × G where E is the total space of a fibre bundle over space-time and G a Lie group acting on E. In this paper, the algebra A is defined in such a way that the m...

On the Universal Covering Space and the Fundamental Group

In this note it will be shown that when A is a retract (cf. [3])1 of X, then the same relationship holds between the universal covering spaces of A and X (Theorem 1.1) and also between the fundamental groups of A and X (Theorem 2.2). We denote the universal covering space of X by X*, where pEX, and the fundamental group by iriX) [l]. All spaces are assumed to be arcwise connected, Hausdorff spa...

Fundamental Steady state Solution for the Transversely Isotropic Half Space

Response of a transversely isotropic 3-D half-space subjected to a surface time-harmonic excitation is presented in analytical form. The derivation of the fundamental solutions expressed in terms of displacements is based on the prefect series of displacement potential functions that have been obtained in the companion paper by the authors. First the governing equations are uncoupled in the cyl...

The Fundamental Interactions in Noncommutative Geometry