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Scattering Amplitudes in Gauge Theories [Pehme köide]

  • Formaat: Paperback / softback, 195 pages, kõrgus x laius: 235x155 mm, kaal: 3285 g, 85 Illustrations, black and white; XV, 195 p. 85 illus., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 883
  • Ilmumisaeg: 20-Feb-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 364254021X
  • ISBN-13: 9783642540219
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  • Formaat: Paperback / softback, 195 pages, kõrgus x laius: 235x155 mm, kaal: 3285 g, 85 Illustrations, black and white; XV, 195 p. 85 illus., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 883
  • Ilmumisaeg: 20-Feb-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 364254021X
  • ISBN-13: 9783642540219

At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge.

These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory.

Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications.

The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.



Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, this book offers a course of concise yet self-contained and course-tested lecture notes, accompanied by numerous exercises and solutions.

Arvustused

Aimed at the advanced graduate student or a practitioner of high energy theory interested in the subject, the book begins with a review of non-abelian gauge theory and its conventional Feynman methods before immediately delving into on-shell recursion relations of BCFW (Britto-Cachazo-Feng-Witten) and factorization properties. Of particular usefulness to the student are the exercises and an entire appendix dedicated to their detailed solutions. (Yang-Hui He, zbMATH 1315.81005, 2015)

1 Introduction and Basics
1(34)
1.1 Lorentz and Poincare Group, Algebra and Representations
1(2)
1.2 Weyl and Dirac Spinors
3(3)
1.3 Non-Abelian Gauge Theories
6(4)
1.4 Scattering Amplitudes and Feynman Rules for Gauge Theories
10(4)
1.5 Massless Particles: Helicity
14(1)
1.6 Spinor Helicity Formalism for Massless Particles
15(3)
1.7 Gluon Polarizations
18(1)
1.8 Fermion Polarizations
19(1)
1.9 Color Decomposition
20(4)
1.10 Color Ordered Feynman Rules and Properties of Color-Ordered Amplitudes
24(3)
1.11 Vanishing Tree Amplitudes
27(2)
1.12 The Four-Gluon Tree-Amplitude
29(3)
1.13 References and Further Reading
32(3)
References
32(3)
2 Tree-Level Techniques
35(46)
2.1 Britto-Cachazo-Feng-Witten (BCFW) On-shell Recursion
35(7)
2.2 The Gluon Three-Point Amplitude
42(1)
2.3 An Example: MHV Amplitudes
43(2)
2.4 Factorization Properties of Tree-Level Amplitudes
45(5)
2.4.1 Factorization on Multi-Particle Poles
46(1)
2.4.2 Absence of Multi-Particle Poles in MHV Amplitudes
46(1)
2.4.3 Collinear Limits
46(2)
2.4.4 Soft Limit
48(2)
2.5 On-shell Recursion for Amplitudes with Massive Particles
50(5)
2.6 Poincare and Conformal Symmetry
55(4)
2.7 N = 4 Super Yang-Mills Theory
59(19)
2.7.1 On-shell Superspace and Superfields
61(2)
2.7.2 Superconformal Symmetry
63(2)
2.7.3 Super-amplitudes, and Extraction of Components
65(3)
2.7.4 Super BCFW-Recursion
68(2)
2.7.5 Three-Point Super-amplitudes
70(1)
2.7.6 Solving the Super-BCFW Recursion: MHV Case
71(3)
2.7.7 Solving the Super-BCFW Recursion: NMHV Case
74(4)
2.8 References and Further Reading
78(3)
References
79(2)
3 Loop-Level Structure
81(66)
3.1 Introduction
81(1)
3.2 Conventions for Minkowski-Space Integrals
82(2)
3.3 General Remarks, Ultraviolet and Infrared Divergences
84(4)
3.3.1 Ultraviolet Divergences
86(1)
3.3.2 Infrared Divergences
86(1)
3.3.3 Regularization Scheme
87(1)
3.4 Integral Reduction
88(14)
3.4.1 The Van Neerven-Vermaseren Basis
90(2)
3.4.2 Reduction of the Integrand in D = 4 - 2ε Dimensions
92(5)
3.4.3 Higher Dimensional Loop Momentum Integration
97(2)
3.4.4 An Example: The Photon Self-Energy in Massless QED
99(3)
3.5 Unitarity
102(25)
3.5.1 Two-Particle Cuts of the Four Gluon Amplitude
103(9)
3.5.2 Generalized Unitarity and Higher-Order Cuts
112(9)
3.5.3 Rational Part: All-Plus Helicity Amplitudes
121(2)
3.5.4 An Example: Higgs Production via Gluon Fusion
123(4)
3.6 Overview of Integration Techniques for Loop Integrals
127(4)
3.6.1 Notation and Dual Coordinates
128(1)
3.6.2 Feynman Parametrization
129(2)
3.7 Mellin-Barnes Techniques
131(5)
3.7.1 Resolution of Singularities in ε
133(1)
3.7.2 Asymptotic Expansions and Resummation
134(1)
3.7.3 Numerical Evaluation and Convergence
135(1)
3.8 Integration by Parts and Differential Equations
136(5)
3.8.1 Integration by Parts Identities
136(1)
3.8.2 Differential Equations
137(2)
3.8.3 Simplified Approach to Differential Equations
139(2)
3.9 References and Further Reading
141(6)
References
143(4)
4 Advanced Topics
147(24)
4.1 Recursion Relations for Loop Integrands
147(5)
4.2 Scattering Amplitudes in N = 4 Super Yang-Mills
152(1)
4.3 Wilson Loop/Scattering Amplitude Duality
153(5)
4.4 (Dual) Conformal Symmetry
158(4)
4.4.1 Conformal Ward Identities for Cusped Wilson Loops
158(2)
4.4.2 Dual Conformal Symmetry of Scattering Amplitudes
160(2)
4.5 Dual Superconformal and Yangian Symmetry
162(3)
4.6 From Correlation Functions to Wilson Loops and Scattering Amplitudes
165(2)
4.7 References and Further Reading
167(4)
References
167(4)
Appendix A Renormalization Properties of Wilson Loops
171(4)
References
173(2)
Appendix B Conventions and Useful Formulae
175
Solutions to the Exercises
177
References
195