A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground state is explicitly computed and we show that it is infinitely degenerated and implying a spontaneous symmetry breaking. The model can be straightforwardly extended to many particles and the main above properties are retained. Possible applications to the Bose-Einstein condensation with dipole-dipole interactions are briefly discussed.
We introduce a new model of spin noncommutative space in which noncommutative extension of the coordinate operators are assumed to be chirality dependent. Noncommutative correspondences of classical fields are defined via Weyl ordering, and the maps are represented by a spin-dependent translation operator. Based on the maps, gauge field theory in chiral spin noncommutative space is established. The corresponding gauge transformations are induced by a local phase rotation on commutative functions, and hence are consistent with the ordinary gauge transformations by definition. Furthermore, a gen…
In this paper, we investigate the bound-state solutions of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in (2+1)-dimensions. We consider a radial magnetic field generated by anti-Helmholtz coils, and the uniform electric field of the Stark effect. Next, we determine the bound-state solutions of the system, given by the two-component Dirac spinor and the relativistic energy spectrum. We note that this spinor is written in terms of the generalized Laguerre polynomials, and this spectrum is a linear function on the potenti…
In this paper, we investigate the thermodynamic properties of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in contact with a heat bath. Using the canonical ensemble, we determine the properties for both relativistic and nonrelativistic cases through the \textit{Euler-MacLaurin} formula in the high temperatures regime. In particular, the main properties are: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. Next, we analyze via 2D graphs the behavior of the properties as a function of temper…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator method. Imposing the additional constraints to eliminate the reduntant degrees of freedom, the noncommutative quantum system with noncommutativity among the coordinates on the curved space is exactly constructed. Then, it is shown that the resultant Hamiltonian contains the quantum corrections in the exact form. We further discuss the additional constraints to…
Beta, Dipole and Noncommutative Deformations of M-theory Backgrounds with One or More Parameters
我们从包含5个U（1）等距的解出发构造新的M-理论解。我们通过沿着5-torus方向之一减少，然后通过O（4，4）矩阵的作用进行T-对偶并提升回11维来做到这一点。特殊的T-对偶变换是嵌入O（4，4）中的O（2，2）变换序列，其中每个O（2，2）的作用给出10维的Lunin-Maldacena变形。当初始11维背景的4-形式沿5-环面最多有一条腿时，我们找到了单参数和多参数变形解的度量和4-形式场的一般公式。新解中的所有变形项都是以5 × 5矩阵的子行列式给出的，该矩阵表示5-环面上的度量。我们将这些结果应用于AdS_r x X^{11-r}型的几个M-理论背景。通过适当的选择的T-对偶和减少方向，我们得到类似的β，偶极和非交换变形。我们还提供了只有3或4个U（1）等距的背景公式，并研究了一个情况下，我们的假设为4-形式的字段被违反。
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized in different physical contexts. Even though are we focused on quantum mechanics in noncommutative space $\textbf{R}_λ^3$, the results can be reconstructed in ordinary quantum mechanics in $\textbf{R}^3$ as well.
