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Biquaternions and ADHM Construction of Non-Compact SL(2,C) Yang-Mills Instantons | | Sheng-Hong Lai
; Jen-Chi Lee
; I-Hsun Tsai
; | | Date: |
3 Dec 2014 | | Abstract: | 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 SL(2,C) SDYM instantons. The number of moduli for SL(2,C)
k-instantons is found to be twice of that of Sp(1), 16k-6. These new SL(2,C)
instanton solutions contain the SL(2,C) (M,N) instanton solutions constructed
previously as a subset. The structure of singularities of the SL(2,C)
1-instanton field configuration with 10 moduli parameters is particularly
investigated. The existence of singular structures of the non-compact SL(2,C)
SDYM field configurations are mathematically consistent with recent results of
the complex ADHM equations. | | Source: | arXiv, 1412.1360 | | Services: | Forum | Review | PDF | Favorites | |
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