Biquaternions and ADHM construction of non-compact SL(2,C) Yang–Mills instantons
Sheng-Hong Lai1*, Jen-Chi Lee1, I-Hsun Tsai2
1Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
2Department of Mathematics, National Taiwan University, Taipei, Taiwan
* presenting author:Sheng-Hong Lai,
We extend quaternion calculation in the ADHM construction of Sp(1) (=SU(2)) self-dual Yang–Mills (SDYM) instantons to the case of biquaternion. We use the biconjugate operation of biquaternion first introduced by Hamilton to construct the non-compact View the MathML source-instantons. The number of parameters of this construction for View the MathML source-instantons is found to be twice of that of Sp(1), 16k−6. These new SL(2,C) instanton solutions contain the View the MathML source instanton solutions constructed previously as a subset. The structures of singularities or jumping lines of the complete View the MathML source instantons with 10, 26, 42 moduli parameters are particularly investigated. The existence of singular structures of the View the MathML source-instantons is mathematically consistent with recent results of solutions of complex ADHM equations. It may also help to clarify the long standing global singularity problems associated with Bäcklund transformations of SU(2) instantons.

Keywords: Biquaternions, Non-compact, ADHM, instantons, Jumping lines