Bosons After Symmetry Breaking in Quantum Field 1st Edition by Fujita, Makoto Hiramoto, Hidenori Takahashi ISBN 978-1606921104 160692110X
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ISBN 10: 160692110X
ISBN 13: 978-1606921104
Author: T. Fujita, Makoto Hiramoto, Hidenori Takahashi
The authors present a unified description of the spontaneous symmetry breaking and its associated bosons in fermion field theory. There is no Goldstone boson in the fermion field theory models of Nambu-Jona-Lasinio, Thirring and QCD2 after the chiral symmetry is spontaneously broken in the new vacuum. The defect of the Goldstone theorem is clarified, and the ‘massless boson’ predicted by the theorem is virtual and corresponds to just a free massless fermion and antifermion pair.Further, the authors discuss the exact spectrum of the Thirring model by the Bethe ansatz solutions, and the analytical expressions of all the physical observables enable the authors to understand the essence of the spontaneous symmetry breaking in depth. Also, the authors examine the boson spectrum in QCD2, and show that bosons always have a finite mass for SU(Nc) colours. The problem of the light cone prescription in QCD2 is discussed, and it is shown that the trivial light cone vacuum is responsible for the wrong prediction of the boson mass.
Table of contents:
1 Introduction
2 Goldstone Theorem and Its Applicability
2.1. Boson Field Theory Model
2.2. Fermion Field Theory Model
3 Goldstone Boson in Boson Field Theory
3.1. Symmetry Breaking in Four Dimensional Boson Fields
3.2. Symmetry Breaking in Two Dimensional Boson Fields
4 No Goldstone Boson in Fermion Field Theory
4.1. Intuitive Discussion
4.2. Bogoliubov Transformation
.4.3. Massive Fermion Case
4.4. Massless Fermion Case
4.5. Boson Mass in NJL Model
4.6. Boson Mass in Thirring Model
5 Bethe Approach Solutions in Thirring Model
5.1. Thirring Model and Bethe Ansatz Solutions
5.2. Vacuum State
5.3. Symmetric Vacuum State
5.4. True Vacuum State
5.5. 1p1h State
5.6. Boson State
5.7. Bosonization of Massless Thirring Model
5.8. Physics of Zero Mode .
5.9. Bosonization of Massive Thirring Model
5.10. Bosons of Massive Thirring Model
5.11. Summary of Thirring Model
6 Schwinger Boson in Two Dimensional QED
6.1. Schwinger Model
6.2. Bosonization of Schwinger Model
6.3. QED2 with Massive Fermions
7 Bosons in Two Dimensional QCD
7.1. Bogoliubov Transformation in QCD2.
7.2. Condensate and Boson Mass in SU (2) and SU(3)
7.3. Condensate and Boson Mass in SU (N)
7.4. QCD2 in Light Cone
7.5. Examination of ‘t Hooft Model
7.6. RPA Calculations in QED2 and QCD2
7.7. Spontaneous Chiral Symmetry Breaking in QCD2
8 Conclusions
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Tags: Fujita, Makoto Hiramoto, Hidenori Takahashi, Bosons After, Breaking in Quantum