A direct link between the Lie group SU(3) and the singular hypersurface $X^{3}+cdots = 0$ via quantum mechanics

Pramana

Siddhartha Sen1 2¹ 

[1] School of Mathematics, Trinity College, Dublin, Ireland$$

关键词: Lie groups;    singularities;    classical phase space.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

A classical phase space with a suitable symplectic structure is constructed together with functions which have Poisson brackets algebraically identical to the Lie algebra structure of the Lie group SU(3). It is shown that in this phase space there are two spheres which intersect at one point. Such a system has a representation as an algebraic curve of the form $X^{3} +cdots = 0$ in $mathscr{C}^{3}$. The curve introduced is singular at the origin in the limit when the radii of the spheres go to zero. A direct connection between the Lie groups SU(3) and a singular curve in $mathscr{C}^{3}$ is thus established. The key step needed to do this was to treat the Lie group as a quantum system and determine its phase space.

【 授权许可】

Unknown