Weyl equation and (non)-commutative SU(n + 1) BPS monopoles
- 31 Downloads
We apply the ADHMN construction to obtain the SU(n + 1) (for generic values of n) spherically symmetric BPS monopoles with minimal symmetry breaking. In particular, the problem simplifies by solving the Weyl equation, leading to a set of coupled equations, whose solutions are expressed in terms of the Whittaker functions. Next, this construction is generalized for non-commutative SU(n + 1) BPS monopoles, where the corresponding solutions are given in terms of the Heun B functions.
KeywordsSolitons Monopoles and Instantons Non-Commutative Geometry
- W. Nahm, The construction of all self-dual multimonopoles by the ADHM method, in Monopoles in quantum field theory, N.S. Craigie et al. eds., World Scientific, Singapore (1982).Google Scholar
- G. Arfken, Mathematical methods for physicists, Academic Press, New York U.S.A. (1985).Google Scholar