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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 ChiralSuperfield)。 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 SupersymmetricNJL model in functional integral approach. The supersymmetric extension of NJLmodel has been a four-supereld interaction model. Our studies highlight some featuresof NJL model and its supersymemtric counter part, the SNJL Model as well asthe HSNJL model which is has a holomorphic dimension 5 interactions and anothermodel of dimension 6 interaction with single chiral supereld. With the feature ofthe eective theories of the mentioned Lagrangian introduced, we looked into thefunctional integral of auxiliary supereld where we investigate the signicance of"integrating out" the auxiliary supereld to see that the establishment of eectivetheories is also equivalent at the quantum level. This followed by the analaysis and interpretationof the approach to provide a full picture in the comparison of functionalintegral and the classical equation of motion of eective theories of the mentionedmodels that was achived by introducing the auxiliary supereld.6
 1 Introduction ------------------------------------12 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----------------------- 73 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----284 Analysis and Interpretation--------------------- 295 Conclusion-------------------------------------- 31Bibliography-------------------------------------- 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 SimpleModel 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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