Ruibin Zhang: Paramanifolds for Green’s generalised quantisation
发布日期:2024-07-01  字号:   【打印



:Ruibin Zhang 教授

工作单位University of Sydney



Herbert S. Green introduced a generalised quantisation in 1953, which gave rise to the celebrated parastatistics that included the standard Bose-Fermi statistics as the special case of order 1. In recent years there have been reports of quantum simulations of para-particles using systems of trapped ions, indicating that some quasi particles observed in condensed matter may indeed be parabosons or parafermions.

Parastatistics has been widely studied mathematically since its inception. However, the following fundamental questions concerning parafermions have not been addressed systematically:

(1) What are the algebras in which the coordinates of parafermions at the classical level are valued in?

(2) What are the spaces whose functions describe classical parafermionic fields?

It is well known that these questions were answered for order 1 parafermions (i.e., usual fermions) by the theory of supermanifolds built with Grassmann algebras.  We generalise the theory to answer the above questions for parafermions of orders greater than 1.


Ruibin Zhang,澳大利亚悉尼大学数学与统计学院教授,澳大利亚数学会副主席。曾获得澳大利亚研究委员会伊丽莎白二世奖学金,澳大利亚研究委员会教授奖等诸多荣誉。研究主要集中在李理论及其在量子物理中的应用,涉及量子(超)群、李超代数、低维拓扑、非交换几何等领域。特别地,在量子代数的结构和表示理论等方面取得了一系列有重要国际影响的研究成果,在包括国际数学顶尖期刊Annals of Mathematics, J.Eur.Math.Soc., Adv.Math, Comm.Math.Phys, Proc.Lond.Math.Soc等重要国际数学刊物上发表140多篇高水平论文,并被国际同行大量引用。