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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 趙挺偉 | |
| dc.contributor.author | Yu-Ying Lee | en |
| dc.contributor.author | 李昱穎 | zh_TW |
| dc.date.accessioned | 2021-06-15T00:24:04Z | - |
| dc.date.available | 2009-02-10 | |
| dc.date.copyright | 2009-02-10 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-01-23 | |
| dc.identifier.citation | [1] J. Schwinger, Phys. Rev. 128 (1962) 2425.
[2] A.V. Smilga, Phys. Rev. D 55 (1997) 443. [3] T. W. Chiu, Phys. Rev. D 58, 074511 (1998) [arXiv:hep-lat/9804016]. [4] T. W. Chiu and S. V. Zenkin, Phys. Rev. D 59, 074501 (1999) [arXiv:heplat/ 9806019]. [5] T. W. Chiu, Phys. Rev. Lett. 90, 071601 (2003) [arXiv:hep-lat/0209153]. [6] T. W. Chiu, arXiv:hep-lat/0303008. [7] T. W. Chiu, Nucl. Phys. Proc. Suppl. 129, 135 (2004) [arXiv:heplat/ 0310043]. [8] K.G. Wilson, Phys. Rev. D 10(1974) 2445 48 [9] K.G. Wilson, ”Quarks and Strings on a lattice”, in New Phenomena in Subnuclear Physics, ed. A. Zinchichi (Plenum Press, New York, 1975), Part A, p.69. [10] H. Nielsen, M. Ninomiya, Nucl. Phys. B 185 (1981) 20. [11] P.H. Ginsparg and K.G. Wilson, ”A Remnant of Chiral Symmetry on the Lattice”, Phys. Rev. D25 (1982) 2649. [12] M. Luscher, ”Exact chiral symmetry on the lattice and the Ginsparg- Wilson relation”, Phys. Lett. B428 (1998) 342 [13] T. W. Chiu, Phys. Lett. B 521 (2001) 429 [arXiv:hep-lat/0110083]. [14] R. Narayanan and H. Neuberger, Phys. Lett. B 302, 62 (1993); Nucl. Phys. B 412, 574 (1994); Phys. Rev. Lett. 71, 3251 (1993); Nucl. Phys. B 443, 305 (1995) [15] H. Neuberger, Phys. Lett. B 417, 141 (1998); Phys. Lett. B 427, 353 (1998) [16] P. Hernadez, K. Jansen, M. Luscher, Nucl. Phys. B552 (1999) 363. [17] D.B. Kaplan, Phys. Lett. B288 (1992) 342. [18] S. Duane, A. D. Kennedy,B. J. Pendleton and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B195(1987) 216. 49 [19] T. W. Chiu et al. [JLQCD and TWQCD Collaborations], PoS LAT2008, 072 (2008) [arXiv:0810.0085 [hep-lat]]. [20] Y. Shamir, Nucl. Phys. B406 (1993) 90. [21] M. F. Atiyah and I. M. Singer, Annals Math. 87, 484 (1968). [22] H. Leutwyler and A. Smilga, Phys. Rev. D 46, 5607 (1992). [23] H. Fukaya and T. Onogi, Phys. Rev. D 70, 054508 (2004) [24] S. Aoki, H. Fukaya, S. Hashimoto and T. Onogi, Phys. Rev. D 76, 054508 (2007) [25] R. Brower, S. Chandrasekharan, J. W. Negele and U. J. Wiese, Phys. Lett. B 560, 64 (2003) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/41590 | - |
| dc.description.abstract | 在這篇論文中，我們應用最佳手則對稱之新費米場作用量(optimal domain-wall fermion)，研究Schwinger模型上的拓樸率。藉由拓樸率的定義，我們可以利用整體拓樸荷(global topological charge)來決定拓樸率。同時，透過鞍點近似法(saddle point expansion)，我們也可以在一個固定的拓樸區(fixed topological sector)內，藉由拓樸密度(topological charge density)的兩點相關係數以得到拓樸率。最後我們將證明在晶格上，這兩種方法會得出相同的拓樸率。 | zh_TW |
| dc.description.abstract | In this thesis, we study the topological susceptibility in the Schwinger model with optimal domain-wall fermions. We obtain the topological susceptibility from counting the global topological charge. Also, using the saddle point
expansion, topological susceptibility can be extracted from the 2-point correlation functions of topological charge density in a fixed topological sector.We can demonstrate that the values obtained from this two methods are in good agreement. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T00:24:04Z (GMT). No. of bitstreams: 1 ntu-98-R95222050-1.pdf: 315528 bytes, checksum: 21dc5a1f6712d2d9a3efb434d4774094 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 1 Introduction 3
1.1 Schwinger Model . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Lattice Formulation of U(1) Gauge Field . . . . . . . . . . . . 6 1.3 Naive Lattice Formulation of Fermion Field . . . . . . . . . . 7 2 Dirac Operator Schemes 10 2.1 Wilson Dirac Operator . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Ginsparg-Wilson relation . . . . . . . . . . . . . . . . . . . . . 11 2.3 Overlap Dirac Operator . . . . . . . . . . . . . . . . . . . . . 13 2.4 Conventional Domain Wall Fermion . . . . . . . . . . . . . . . 16 2.5 Optimal Domain Wall Fermion . . . . . . . . . . . . . . . . . 18 3 Monte Carlo Method 22 3.1 Fermion Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Pseudo-Fermion Field . . . . . . . . . . . . . . . . . . . . . . . 24 1 3.3 Hybrid Monte Carlo Method . . . . . . . . . . . . . . . . . . . 25 4 Topological Susceptibility 29 4.1 Topological Charge On the Lattice . . . . . . . . . . . . . . . 29 4.2 Topological Susceptibility On the Lattice . . . . . . . . . . . . 31 4.3 Fixed Topological Sector . . . . . . . . . . . . . . . . . . . . 31 5 Data Analysis 35 5.1 Autocorrelations in Monte Carlo simulation time . . . . . . . . 35 5.2 Data Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3 Jackknife Method . . . . . . . . . . . . . . . . . . . . . . . . . 37 6 Results 38 6.1 Topological Susceptibility from Global Topological Charge . . 38 6.2 Topological Susceptibility from Fixed Topological Sector . . . 42 7 Conclusion 46 Bibliography 48 A Force in Hybrid Monte Carlo 51 A.1 Gauge Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 A.2 Fermion Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 | |
| dc.language.iso | en | |
| dc.subject | 拓樸荷 | zh_TW |
| dc.subject | 拓樸 | zh_TW |
| dc.subject | 晶格 | zh_TW |
| dc.subject | 二維場論 | zh_TW |
| dc.subject | 場論 | zh_TW |
| dc.subject | 拓樸率 | zh_TW |
| dc.subject | topology | en |
| dc.subject | topological charge | en |
| dc.subject | topoligical susceptibility | en |
| dc.title | Schwinger模型上的拓樸率 | zh_TW |
| dc.title | Topological Susceptibility in the Schwinger Model | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 高涌泉,謝東翰 | |
| dc.subject.keyword | 拓樸,晶格,二維場論,場論,拓樸率,拓樸荷, | zh_TW |
| dc.subject.keyword | topology,topoligical susceptibility,topological charge, | en |
| dc.relation.page | 53 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-01-23 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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