奇异Newton-Hooke群、非对易平面与超共形对称
Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
摘要：
本文研究了2+1维时空中具有奇异对称性的系统。在奇异结构中编码，出现了非对易坐标和相结构。这类系统分别引起了物理学不同领域的关注。其中，我们可以提到：理论的射线表示李群，任何子物理，一些凝聚态系统，例如量子霍尔效应，平面规范和引力理论，非对易场论，非对易几何，和非对易量子力学。我们主要研究奇异非相对论对称性，如奇异Newton-Hooke群，奇异非相对论对称性与非对易Landau问题的关系，非对易Landau问题的对称性及其超对称扩张。奇异的牛顿-胡克群对应于德西特群的非相对论极限，并且具有奇异的伽利略群作为特殊的平坦极限。对于奇异的Newton-Hooke对称性，我们构造了一个自由粒子作用量，实现了对它的经典和量子性质的完整研究。Newton-Hooke系统与非对易Landau问题密切相关，我们将分别研究。我们表明，列入自旋自由度的非对易朗道问题产生的自然整合的异国情调的牛顿-虎克群的共形对称性和超对称性。
英文摘要：
In this thesis some systems with exotic symmetries, which are a peculiarity in 2+1 space-time dimensions, are studied. Coded in the exotic structure, there appear noncommutative coordinates and a phases structure. This kind of systems has attracted attention from different areas of physics independently. Among them, we can mention: theory of ray representations of Lie groups, anyon physics, some condensed matter systems, for instance the quantum Hall effect, planar gauge and gravitation theories, noncommutative field theory, noncommutative geometry, and noncommutative quantum mechanics. We focus our study in some topics on exotic nonrelativistic symmetries, such as the exotic Newton-Hooke group, the relation between such systems and the noncommutative Landau problem, the symmetries of noncommutative Landau problem, and of its supersymmetric extension. The exotic Newton-Hooke group corresponds to the nonrelativistic limit of the de Sitter groups, and has as a particular, flat limit the exotic Galilei group. For the exotic Newton-Hooke symmetry, we construct a free particle action, and realize a complete study of its classical and quantum properties. The Newton-Hooke system is intimately related with the noncommutative Landau problem, which we study apart. We show that the inclusion of spin degrees of freedom in the noncommutative Landau problem produces a natural integration of the exotic Newton-Hooke group with the conformal symmetry and supersymmetry.
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