Browsing by Author "Tsai, I-Hsun"

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Biquaternions and ADHM construction of non-compact SL(2, C) Yang-Mills instantons
(2015-10-01)
Lai, Sheng-Hong
;
Lee, Jen-Chi
;
Tsai, I-Hsun
;
電子物理學系
;
Department of Electrophysics
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) k-instantons. The number of parameters of this construction 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 structures of singularities or jumping lines of the complete SL(2, C) k = 1, 2, 3 instantons with 10, 26, 42 moduli parameters are particularly investigated. The existence of singular structures of the SL(2, C) k-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 Backlund transformations of SU(2) instantons. (C) 2015 Elsevier Inc. All rights reserved.
Extended complex Yang-Mills instanton sheaves
(2020-03-01)
Lai, Sheng-Hong
;
Lee, Jen-Chi
;
Tsai, I-Hsun
;
電子物理學系
;
Department of Electrophysics
In the search of Yang-Mills (YM) instanton sheaves with topological charge two, the rank of beta matrix in the monad construction can be dropped from the bundle case with rank beta = 2 to either rank beta = 1 [S. H. Lai, J. C. Lee and I. H. Tsai, Yang Mills instanton sheaves, Ann. Phys. 377 (2017) 446] or 0 on some points of CP3 of the sheaf cases. In this paper, we first show that the sheaf case with rank beta = 0 does not exist for the previous construction of SU(2) complex YM instantons [S. H. Lai, J. C. Lee and I. H. Tsai, Biquaternions and ADHM construction of concompact SL(2, C) Yang-Mills instantons, Ann. Phys. 361 (2015) 14]. We then show that in the new "extended complex YM instantons" discovered in this paper, rank beta can be either 2 on the whole CP3 (bundle) with some given ADHM data or 1, 0 on some points of CP3 with other ADHM data (sheaves). These extended SU(2) complex YM instantons have no real instanton counterparts. Finally, the potential applications to real physics systems are noted in the end of the paper.
Sheaf lines of Yang-Mills instanton sheaves
(2019-03-01)
Lai, Sheng-Hong
;
Lee, Jen-Chi
;
Tsai, I-Hsun
;
電子物理學系
;
Department of Electrophysics
We calculate a sheaf line in CP3 which is the real line supporting sheaf points on CP3 of SL(2, C) Yang-Mills (YM) instanton (or SU(2) complex YM instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over S-4 spacetime. In addition, we calculate the singularity structure of the connection A and the field strength F at the corresponding singular point on S-4 of this sheaf line. We found that the order of singularity at the singular point on S-4 associated with the sheaf line in CP3 is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines.
Yang-Mills instanton sheaves
(2017-02-01)
Lai, Sheng-Hong
;
Lee, Jen-Chi
;
Tsai, I-Hsun
;
電子物理學系
;
Department of Electrophysics
The SL(2, C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the monad construction. Moreover, we discover that, in addition to the holomorphic vector bundles on CP3 similar to the case of SU(2) ADHM construction, the SL(2, C) instanton solutions can be used to explicitly construct instanton sheaves on CP3. Presumably, the existence of these instanton sheaves is related to the singularities of the SL(2, C) instantons on S-4 which do not exist for SU(2) instantons. (C) 2016 Elsevier Inc. All rights reserved.
Yang-Mills instanton sheaves with higher topological charges
(2019-07-01)
Lai, Sheng-Hong
;
Lee, Jen-Chi
;
Tsai, I-Hsun
;
電子物理學系
;
Department of Electrophysics
We explicitly construct SL(2, C) (or SU(2) complex) Yang-Mills (YM) (weakly) three and four instanton sheaves on CP3. These results extend the previous construction of YM (weakly) instanton sheaves with topological charge two [S. H. Lai, J. C. Lee and I. H. Tsai, Yang-Mills instanton sheaves, Ann. Phys. 377 (2017) 446, arXiv: 1603.02860].