## Quaternionic wavefunctions of unconventional BECs and high dimensional Landau le

Quaternions are a natural extension of complex number, which are the first discovered non-commutative division algebra. Quaternions were invented by Hamilton in 1843, and Hamilton spent the last twenty years of his life to promote this beautiful mathematical concept, but only with partial success. In this talk, I will discuss the application of quaternions in spin-orbit coupled BECs and high dimensional Landau levels. Essentially they are SU(2) generalizations of their usual U(1) counterparts. Quaternionic phase defects are identified in the spin-orbit coupled BECs. And the 3D and 4D Landau levels exhibit quaternionic analyticity.
Yi Li, and Congjun Wu (in collaboration with Xiangfa Zhou)