Noncommutative Geometry of Phase Space

Representation of Noncommutative Phase Space

The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Schödinger equation from noncommutative space to commutative space is obtained. PACS number: 03.65Bz, 11.90.+t

Noncommutative Geometry and Compactifications of the Moduli Space of Curves

In this paper we show that the homology of a certain natural compactification of the moduli space, introduced by Kontsevich in his study of Witten’s conjectures, can be described completely algebraically as the homology of a certain differential graded Lie algebra. This two-parameter family is constructed by using a Lie cobracket on the space of noncommutative 0-forms, a structure which corresp...

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...

Strings , Noncommutative Geometry and the Size of the Target Space

We describe how the presence of the antisymmetric tensor (tor-sion) on the world sheet action of string theory renders the size of the target space a gauge non invariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d, d, Z). The crucial point is that, with a transformation , it is possible always to have all of the lowest eigenvalue...

Noncommutative geometry