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Effective Lagrangians for the Standard Model [Hardback]

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  • Formāts: Hardback, 335 pages, 33 figures, 7 tables
  • Sērija : Texts and Monographs in Physics
  • Izdošanas datums: 30-Sep-1997
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540625704
  • ISBN-13: 9783540625704
Citas grāmatas par šo tēmu:
Effective Lagrangians for the Standard ModelPalielināt
  • Formāts: Hardback, 335 pages, 33 figures, 7 tables
  • Sērija : Texts and Monographs in Physics
  • Izdošanas datums: 30-Sep-1997
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540625704
  • ISBN-13: 9783540625704
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783540625704.html
Keywords:
This is a detailed and pedagogical exposition of the effective Lagrangian techniques and their applications to high-energy physics. It covers the main theoretical ideas and describes how to use them in different fields, such as chiral perturbation theory and the symmetry breaking sector of the standard model and even low-energy quantum gravity. The book is written in the language of modern quantum field theory. Some of the theoretical topics treated are: decoupling; the Goldstone theorem; the non-linear model; anomalies; the Wess-Zumino-Witten term; and the equivalence theorem.
1. The Notion of Effective Lagrangian
1(22)
1.1 Introduction
1(3)
1.2 Integration of the Heavy Modes
4(5)
1.2.1 The Effective Action for the Light Modes
4(2)
1.2.2 Low Energy Expansions
6(3)
1.3 The Decoupling Theorem
9(2)
1.4 The Euler-Heisenberg Lagrangian
11(3)
1.5 Theories with Spontaneous Symmetry Breaking
14(3)
1.6 Decoupling of Chiral Fermions
17(4)
1.7 References
21(2)
2. Global Symmetries in Quantum Field Theory
23(18)
2.1 Classical Symmetries
23(5)
2.2 Green Functions and the Reduction Formula
28(2)
2.3 Quantum Symmetries and Ward Identities
31(2)
2.4 Spontaneous Symmetry Breaking and the Goldstone Theorem
33(4)
2.5 Explicit Symmetry Breaking and the Dashen Conditions
37(2)
2.6 References
39(2)
3. The Non-linear XXX Model
41(18)
3.1 Introduction
41(1)
3.2 The Geometry and the Dynamics of the Non-linear XXX Model
42(4)
3.3 The Quantum Non-linear XXX Model
46(2)
3.4 Reparametrization Invariance of the S-Matrix Elements
48(1)
3.5 Local Symmetries and the Higgs Mechanism
49(5)
3.6 Topologically Non-trivial Configurations
54(3)
3.7 References
57(2)
4. Anomalies
59(38)
4.1 Introduction
59(1)
4.2 The Axial Anomaly, Triangle Diagrams and the XXX(0) Decay
60(5)
4.3 The Axial Anomaly and the Index Theorem
65(3)
4.4 Gauge Anomalies
68(5)
4.4.1 The Wess-Zumino Consistency Conditions
72(1)
4.5 Regularization Methods
73(3)
4.6 Ambiguities and Counterterms
76(2)
4.7 Topological Interpretation of Non-Abelian Anomalies
78(5)
4.8 Non-perturbative Anomalies
83(2)
4.9 Non-linear XXX Model Anomalies
85(1)
4.10 The Wess-Zumino-Witten Term
86(7)
4.10.1 Anomalous Processes in QCD
86(1)
4.10.2 The Non-local Anomalous Effective Action
87(2)
4.10.3 The WZW Term with Gauge Fields
89(2)
4.10.4 Anomalous Processes and the WZW Term
91(1)
4.10.5 The SU(2) WZW Term
92(1)
4.11 The Trace Anomaly
93(2)
4.12 References
95(2)
5. The Symmetries of the Standard Model
97(28)
5.1 The Elements of the Standard Model
97(6)
5.1.1 Matter
97(1)
5.1.2 Gauge Fields
98(3)
5.1.3 The Symmetry Breaking Sector
101(2)
5.2 The Cabibbo-Kobayashi-Maskawa Matrix and Weak CP Violation
103(2)
5.3 The Cancellation of Gauge Anomalies in the Standard Model
105(4)
5.4 Baryon and Lepton Number Anomalies in the Standard Model
109(2)
5.5 The Evolution of the Coupling Constants
111(2)
5.6 The Strong CP Problem
113(8)
5.6.1 The XXX-Vacuum
115(2)
5.6.2 The Role of Instantons
117(2)
5.6.3 The Strong CP Problem
119(2)
5.7 The Symmetries of the Standard Model
121(2)
5.8 References
123(2)
6. The Effective Lagrangian for QCD
125(50)
6.1 The QCD Lagrangian
125(3)
6.2 QCD at Low Energies
128(2)
6.3 The Chiral Lagrangian at Leading Order
130(5)
6.4 The Chiral Lagrangian to Next to Leading Order
135(7)
6.4.1 The L(4) Lagrangian
135(1)
6.4.2 One-Loop Renormalization
136(3)
6.4.3 The Effective Action to One Loop
139(3)
6.5 The Low-Energy Constants
142(9)
6.5.1 Phenomenological Estimates
142(3)
6.5.2 Theoretical Estimates
145(4)
6.5.3 The N(f) = 2 Case
149(2)
6.6 The Problem of Unitarity in ChPT
151(20)
6.6.1 Unitarity and Dispersion Relations
153(8)
6.6.2 The Large-N Limit
161(10)
6.7 References
171(4)
7. The Standard Model Symmetry Breaking Sector
175(54)
7.1 The Mass Problem
175(4)
7.2 The Effective Lagrangian for the SM Symmetry Breaking Sector
179(3)
7.3 The O(p(4)) Lagrangian and One-Loop Renormalization
182(7)
7.3.1 The O(p(4)) Lagrangian
182(3)
7.3.2 The Covariant Formalism
185(1)
7.3.3 One-Loop Renormalization
186(3)
7.4 The Heavy Higgs and QCD-Like Models
189(4)
7.4.1 The Heavy Higgs Model
189(3)
7.4.2 QCD-Like Models
192(1)
7.5 Phenomenological Determination of the Chiral Parameters
193(8)
7.5.1 Precision Tests of the Standard Model (Oblique Corrections)
194(2)
7.5.2 The Trilinear Gauge Boson Vertex
196(1)
7.5.3 Elastic Gauge Boson Scattering
197(4)
7.6 The Equivalence Theorem
201(15)
7.6.1 Introduction
201(1)
7.6.2 The Slavnov-Taylor Identities
202(6)
7.6.3 The Reduction Formula
208(2)
7.6.4 The Generalized Equivalence Theorem
210(1)
7.6.5 The Equivalence Theorem
211(5)
7.7 The Applicability of the Equivalence Theorem
216(2)
7.8 Gauge Boson Scattering at High Energies
218(8)
7.8.1 Dispersion Relations for the SM Symmetry Breaking Sector
220(1)
7.8.2 The Large-N Limit: The Higgs and the General Case
221(5)
7.9 References
226(3)
8. Gravity and the Standard Model
229(30)
8.1 Introduction
229(2)
8.2 The Standard Model in Curved Space-Time
231(5)
8.3 Anomalies in the Standard Model
236(7)
8.3.1 The Leptonic and Baryonic Anomalies
237(1)
8.3.2 Gauge Anomalies
238(2)
8.3.3 Gravitational Anomalies
240(2)
8.3.4 Charge Quantization in the SM
242(1)
8.4 The Effect of Matter Fields on Gravitation
243(3)
8.5 The Effective Action for Gravity
246(10)
8.5.1 The Background Field Method in Quantum Gravity
246(1)
8.5.2 General Effective Formalism
247(4)
8.5.3 Quantum Corrections to the Newton Potential
251(3)
8.5.4 Perspectives and Other Approaches
254(2)
8.6 References
256(3)
A. Useful Formulae and Notation
259(4)
A.1 Notation in Minkowski Space-Time
259(2)
A.2 Notation in Euclidean Space-Time
261(1)
A.3 Useful Formulae
262(1)
B. Notes on Differential Geometry
263(16)
B.1 Riemannian Geometry
263(6)
B.2 Homogeneous Spaces
269(1)
B.3 The Geometry of Gauge Fields
270(9)
B.4 References
279(1)
C. Aspects of Quantum Field Theory
279(23)
C.1 Renormalization Group Equations
279(8)
C.2 Quantization of Gauge Theories and BRS Invariance
287(6)
C.3 The Background Field Method
293(5)
C.4 The Heat-Kernel Method
298(3)
C.5 References
301(1)
D. Unitarity and Partial Waves
302(9)
D.1 Unitarity
302(1)
D.2 Dispersion Relations
303(3)
D.3 NGB Amplitudes to O(p(4))
306(3)
D.4 References
309(2)
Subject Index 311