Browsing by Author "Lai, Sheng-Hong"

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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.
SL(2, C) Instanton Sheaves
(2017-01-01)
Lai, Sheng-Hong
;
電子物理學系
;
Department of Electrophysics
We constructed SL(2, C) Yang-Mills instanton solutions which satisfy the complex ADHM equations and the monad construction by using the biquaternion method. And we also found that the SL(2, C) instanton solutions can be used to explicitly construct instanton sheaves on CP3 which similar to the case holomorphic vector bundles on CP3 of SU(2) ADHM construction. And the existence of these instanton sheaves is related to singularities on S4 which do not exist in SU(2) instanton case.
Solving Lauricella string scattering amplitudes through recurrence relations
(2017-09-26)
Lai, Sheng-Hong
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Lee, Jen-Chi
;
Lee, Taejin
;
Yang, Yi
;
電機學院
We show that there exist in finite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these in finite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously to all kinematic regimes.
Spin polarization independence of hard polarized fermion string scattering amplitudes
(2019-10-10)
Lai, Sheng-Hong
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Lee, Jen-Chi
;
Yang, Yi
;
電子物理學系
;
Department of Electrophysics
We calculate a class of polarized fermion string scattering amplitudes (PFSSA) at arbitrary mass levels. We discover that, in the hard scattering limit, the functional forms of the non-vanishing PFSSA at each fixed mass level are independent of the choices of spin polarizations. This result agrees with Gross conjecture on high energy string scattering amplitudes extended to the fermionic sector. In addition, this peculiar property of hard PFSSA is to be compared with the usual spin polarization dependence of the hard polarized fermion field theory scatterings. (C) 2019 The Author(s). Published by Elsevier B.V.
The Lauricella functions and exactstring scattering amplitudes
(2016-11-10)
Lai, Sheng-Hong
;
Lee, Jen-Chi
;
Yang, Yi
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電子物理學系
;
Department of Electrophysics
We discover that the 26D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated SL(K + 3, C) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations first conjectured by Gross [1-5] and later corrected and proved in [6-12] in the hard scattering limit, the recurrence relations in the Regge scattering limit with associated SL(5,C) symmetry [24-26] and the extended recurrence relations in the nonrelativistic scattering limit with associated SL(4,C) symmetry [29] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.
The SL(K+3, C) symmetry of the bosonic string scattering amplitudes
(2019-04-01)
Lai, Sheng-Hong
;
Lee, Jen-Chi
;
Yang, Yi
;
電子物理學系
;
Department of Electrophysics
We discover that the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K + 3, C) group. In addition, we find that the K + 2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K + 3, C) group with rank K + 2. As a result, the SL(K + 3, C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the SL(K + 3, C) group can be used to directly prove Gross conjecture [1-3], which was previously corrected and proved by the method of decoupling of zero norm states [4-10]. (C) 2019 The Author(s). Published by Elsevier B.V.
The string BCJ relations revisited and extended recurrence relations of nonrelativistic string scattering amplitudes
(2016-05-31)
Lai, Sheng-Hong
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Lee, Jen-Chi
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Yang, Yi
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電子物理學系
;
Department of Electrophysics
We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s - t and t - u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
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].