Program

O.16 -- Oral, NCTP-41

Date: Wednesday, 3 August 2016

Time: 10h50 - 11h10

Octonionic representation of the nine-dimensional Micz-Kepler problem

Le Dai Nam (1), Le Van Hoang (2)

(1) Atomic Molecular and Optical Research Group, Ton Duc Thang University, 19, Nguyen Huu Tho Street, Tan Phong Ward, District 7, Ho Chi Minh City (2) Ho Chi Minh City University of Pedagogy, 280, An Duong Vuong Street, District 5, Ho Chi Minh City

In previous works, it was proved that the connection between the $2^{h+1}$-dimensional isotropic harmonic oscillator problem and the $(2h+1)$-dimensional MICZ-Kepler problem via the h-th Hurwitz transformation can be established only for. On other hand, each h-th Hurwitz transformations is directly related to the h-th normed division algebra. In present report, we consider the last case where the generalized Hurwitz transformation can be represented by the last normed division algebra, octonion. By using the above-mentioned connection, we can describe the nine dimensional MICZ-Kepler problem in the octonionic representation. Some discussions about the SO(8) monopoles are carried out in the light of the connection between the 16-dimensional isotropic harmonic oscillator and the 9-dimensional MICZ-Kepler problems by the normed division algebras.

Presenter: Lê Đại Nam