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研究生:彭熯豐
研究生(外文):PANG HARN FUNG
論文名稱(外文):Effective Theories for Supersymmetric Nambu-Jona-Lasinio Models established through Functional Integration
指導教授:江祖永
指導教授(外文):Otto C.W. Kong
學位類別:碩士
校院名稱:國立中央大學
系所名稱:物理學系
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:49
中文關鍵詞:NJL模型超對稱四維超場泛函積分單手性超場
外文關鍵詞:NJL ModelSupersymmetrySuperfieldFunctional IntegralChiral Superfield
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本文主要是用泛函積分(Functional Integral)來研究超對稱
NJL 的有效理論。 而NJL 模型在超對稱擴展就是四維超場
(Superfield)的交互作用模型。 我們的研究也著重在NJL 模
型 的特徵和超對稱的對應,SNJL 模型與HSNJL 模式分別
是全純維度5 交互作用與維度6 的單手性超場(Single Chiral
Superfield)。 這裡我們需要引入拉格朗日有效理論的特點,
我們研究了輔性超場(Auxiliary Superfield)的泛函積分與意義
而我們認為有效理論是等價量子層級的。 以下我們透過輔
性超場來分析與說明古典的運動方程對比泛函積分的有效
理。
The main purpose of this thesis is to study the eective theories of Supersymmetric
NJL model in functional integral approach. The supersymmetric extension of NJL
model has been a four-supereld interaction model. Our studies highlight some features
of NJL model and its supersymemtric counter part, the SNJL Model as well as
the HSNJL model which is has a holomorphic dimension 5 interactions and another
model of dimension 6 interaction with single chiral supereld. With the feature of
the eective theories of the mentioned Lagrangian introduced, we looked into the
functional integral of auxiliary supereld where we investigate the signicance of
"integrating out" the auxiliary supereld to see that the establishment of eective
theories is also equivalent at the quantum level. This followed by the analaysis and interpretation
of the approach to provide a full picture in the comparison of functional
integral and the classical equation of motion of eective theories of the mentioned
models that was achived by introducing the auxiliary supereld.
6
1 Introduction ------------------------------------1

2 Background---------------------------------------3
2.1 Nambu-Jona-Lasinio (NJL) MODEL ---------------3
2.2 SNJL Model -----------------------------------4
2.3 HSNJL Model ----------------------------------5
2.4 SNJL Model with a Real Supereld Composite---- 6
2.5 Auxiliary Field Method----------------------- 7

3 Functional Integration of Auxiliary Supereld---- 9
3.1 HSNJL MODEL---------------------------------- 9
3.1.1 Components expansion of HSNL Lagrangian----10
3.1.2 Full Supereld picture of HSNJL Lagrangian--13
3.2 SNJL MODEL----------------------------------- 14
3.2.1 Components expansion of SNJL Lagrangian--- 14
3.2.2 Full Supereld picture of SNJL Lagrangian---20
3.3 SNJL Model with a Real Supereld Composite---- 23
3.3.1 Components expansion of the Lagrangian-----23
3.3.2 Full Supereld picture of the Lagrangian----28

4 Analysis and Interpretation--------------------- 29

5 Conclusion-------------------------------------- 31

Bibliography-------------------------------------- 39
[1] Y. Nambu, Nobel Lecture: Spontaneous Symemtry Breaking in Particle Physics: A Case of Cross Fertilization, Int. J. Mod. Phys. A 24, 2371 (2009), Rev. Mod. Phys. 81 1015 (2009).

[2] Y. Nambu and G. Jona-Lasinio, Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I, Phys. Rev. 122 (1961) 345; Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II, ibid 124 (1961) 246.

[3] T. Kashiwa, Y. Ohnuki, M. suzuki, Path Integral Methods, Clarendon Press, Oxford. (1997).

[4] M. Suzuki Approximate gauge symmetry of composite vector bosons, Phys. Rev. D 82, 045026 (2010)

[5] W. Buchmuller and S. T. Love, Chiral Symmetry and Supersymmetry in the Nambu-Jona-Lasinio Model, Nucl. Phys. B204, 213 (1982)

[6] W. Buchmuller and U. Ellwanger, On the Structure of Composite Goldstino Supermultiplets, Nucl. Phys. B 245, 237 (1984)

[7] D. W. Jung, O. C. W. Kong and J. S. Lee, Holomorphic Supersymmetric Nambu-Jona-Lasinio Model with Application to Dynamical Electroweak Symmetry Breaking], Phys. Rev. D 81, 031701 (2010)

[8] G. Faisel, D. W. Jung and O. C. W. Kong, Dynamical Symmtery Breaking with Four-Supereld Interactions, JHEP 1201, 164 (2012)
48

[9] D. Yan-Min, G. Faisel, D. W. Jung and O. C. W. Kong, Majorana versus Dirac Mass from Holomorphic Supersymmetric Nambu-Jona-Lasinio Model, Phys. Rev. D 87, 085033 (2013)

[10] Y. Cheng, Y. M. Dai, G. Faisel and O. C. W. Kong, A Simple
Model of Dynamical Supersymmetry Breaking with the Generation of Soft Mass(es), arXiv:1507.01514 [hep-ph], submitted to Phys. Rev. Lett. (2015)

[11] Y. Cheng, Y. M. Dai, G. Faisel and O. C. W. Kong, Analysis on a Nambu-Jona-Lasinio Model of Dynamical Supersymemtry Breaking, arXiv:1603.00724 [hep-th].(2016)

[12] W. Siegel, The Auxiliary Field Problem, Physica D 15, 208 (1985).

[13] J. Wess and J. Bagger, Supersymmetry and Supergravity, Princeton, USA: Univ. Pr. (1992)

[14] S. J. Gates, M. T. Grisari, M. Rocek and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys. no: 58, Addison-Wesley (1983).
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