Download Supersymmetry Demystified: A Self-Teaching Guide (Demystified Series) PDF

TitleSupersymmetry Demystified: A Self-Teaching Guide (Demystified Series)
File Size2.8 MB
Total Pages496
Table of Contents
Chapter 1 Introduction
	1.1 What is Supersymmetry, and Why is it Exciting (the Short Version)?
	1.2 What This Book is and What it is Not
	1.3 Effective Field Theories, Naturalness, and the Higgs Mass
	1.4 Further Reading
Chapter 2 A Crash Course on Weyl Spinors
	2.1 Brief Review of the Dirac Equation and of Some Matrix Properties
	2.2 Weyl versus Dirac Spinors
	2.3 Helicity
	2.4 Lorentz Transformations and Invariants
	2.5 A First Notational Hurdle
	2.6 Building More Lorentz Invariants Out of Weyl Spinors
	2.7 Invariants Containing Lorentz Indices
	2.8 A Useful Identity
	2.9 Introducing a New Notation
	2.10 Quiz
Chapter 3 New Notation for the Components of Weyl Spinors
	3.1 Building Lorentz Invariants
	3.2 Index-Free Notation
	3.3 Invariants Built Out of Two Left-Chiral Spinors
	3.4 The ∈ Notation for ±iσ[sup(2)]
	3.5 Notation for the Indices of σ[sup(μ)] and σ[sup(μ)]
	3.6 Quiz
Chapter 4 The Physics of Weyl, Majorana, and Dirac Spinors
	4.1 Charge Conjugation and Antiparticles for Dirac Spinors
	4.2 CPT Invariance
	4.3 A Massless Weyl Spinor
	4.4 Adding a Mass: General Considerations
	4.5 Adding a Mass: Dirac Spinors
	4.6 The QED Lagrangian in Terms of Weyl Spinors
	4.7 Adding a Mass: Majorana Spinors
	4.8 Dirac Spinors and Parity
	4.9 Definition of the Masses of Scalars and Spinor Fields
	4.10 Adding a Mass: Weyl Spinor
	4.11 Relation Between Weyl Spinors and Majorana Spinors
	4.12 Quiz
Chapter 5 Building the Simplest Supersymmetric Lagrangian
	5.1 Dimensional Analysis
	5.2 The Transformation of the Fields
	5.3 Transformation of the Lagrangian
	5.4 Quiz
Chapter 6 The Supersymmetric Charges and Their Algebra
	6.1 Charges: General Discussion
	6.2 Explicit Representations of the Charges and the Charge Algebra
	6.3 Finding the Algebra Without the Explicit Charges
	6.4 Example
	6.5 The SUSY Algebra
	6.6 Nonclosure of the Algebra for the Spinor Field
	6.7 Introduction of an Auxiliary Field
	6.8 Closure of the Algebra
	6.9 Quiz
Chapter 7 Applications of the SUSY Algebra
	7.1 Classification of States Using the Algebra: Review of the Poincaé Group
	7.2 Effects of the Supercharges on States
	7.3 The Massless SUSY Multiplets
	7.4 Massless SUSY Multiplets and the MSSM
	7.5 Two More Important Results
	7.6 The Algebra in Majorana Form
	7.7 Obtaining the Charges from Symmetry Currents
	7.8 Explicit Supercharges as Quantum Field Operators
	7.9 The Coleman-Mandula No-Go Theorem
	7.10 The Haag-Lopuszanski-Sohnius Theorem and Extended SUSY
	7.11 Quiz
Chapter 8 Adding Interactions: The Wess-Zumino Model
	8.1 A Supersymmetric Lagrangian With Masses and Interactions
	8.2 A More General Lagrangian
	8.3 The Full Wess-Zumino Lagrangian
	8.4 The Wess-Zumino Lagrangian in Majorana Form
	8.5 Quiz
Chapter 9 Some Explicit Calculations
	9.1 Refresher About Calculations of Processes in Quantum Field Theory
	9.2 Propagators
	9.3 One Point Function
	9.4 Propagator of the B Field to One Loop
	9.5 Putting It All Together
	9.6 A Note on Nonrenormalization Theorems
	9.7 Quiz
Chapter 10 Supersymmetric Gauge Theories
	10.1 Free Supersymmetric Abelian Gauge Theory
	10.2 Introduction of the Auxiliary Field
	10.3 Review of Nonabelian Gauge Theories
	10.4 The QCD Lagrangian in Terms of Weyl Spinors
	10.5 Free Supersymmetric Nonabelian Gauge Theories
	10.6 Combining an Abelian Vector Multiplet With a Chiral Multiplet
	10.7 Eliminating the Auxiliary Fields
	10.8 Combining a Nonabelian Gauge Multiplet With a Chiral Multiplet
	10.9 Quiz
Chapter 11 Superspace Formalism
	11.1 The Superspace Coordinates
	11.2 Example of Spacetime Translations
	11.3 Supersymmetric Transformations of the Superspace Coordinates
	11.4 Introduction to Superfields
	11.5 Aside on Grassmann Calculus
	11.6 The SUSY Charges as Differential Operators
	11.7 Constraints and Superfields
	11.8 Quiz
Chapter 12 Left-Chiral Superfields
	12.1 General Expansion of Left-Chiral Superfields
	12.2 SUSY Transformations of the Component Fields
	12.3 Constructing SUSY Invariants Out of Left-Chiral Superfields
	12.4 Relation Between the Superpotential in Terms of Super.elds and the Superpotential of Chapter 8
	12.5 The Free Part of the Wess-Zumino Model
	12.6 Why Does It All Work?
	12.7 Quiz
Chapter 13 Supersymmetric Gauge Field Theories in the Superfield Approach
	13.1 Abelian Gauge Invariance in the Superfield Formalism
	13.2 Explicit Interactions Between a Left-Chiral Multiplet and the Abelian Gauge Multiplet
	13.3 Lagrangian of a Free Supersymmetric Abelian Gauge Theory in Superfield Notation
	13.4 The Abelian Field-Strength Superfield in Terms of Component Fields
	13.5 The Free Abelian Supersymmetric Lagrangian from the Superfield Approach
	13.6 Supersymmetric QED
	13.7 Supersymmetric Nonabelian Gauge Theories
	13.8 Quiz
Chapter 14 SUSY Breaking
	14.1 Spontaneous Supersymmetry Breaking
	14.2 F-Type SUSY Breaking
	14.3 The O’Raifeartaigh Model
	14.4 Mass Spectrum: General Considerations
	14.5 Mass Spectrum of the O’Raifeartaigh Model for Μ[sup(2) ≥ 2g2Μ[sup(2)]
	14.6 The Supertrace
	14.7 D-Type SUSY Breaking
	14.8 Second Example of D-Type SUSY Breaking
	14.9 Explicit SUSY Breaking
	14.10 Quiz
Chapter 15 Introduction to the Minimal Supersymmetric Standard Model
	15.1 Lightning Review of the Standard Model
	15.2 Spontaneous Symmetry Breaking in the Standard Model
	15.3 Aside on Notation
	15.4 The Left-Chiral Superfields of the MSSM
	15.5 The Gauge Vector Superfields
	15.6 The MSSM Lagrangian
	15.7 The Superpotential of the MSSM
	15.8 The General MSSM Superpotential
	15.9 Quiz
Chapter 16 Some Phenomenological Implications of the MSSM
	16.1 Supersymmetry Breaking in the MSSM
	16.2 The Scalar Potential, Electroweak Symmetry Breaking, and All That
	16.3 Finding a Minimum
	16.4 The Masses of the Gauge Bosons
	16.5 Masses of the Higgs
	16.6 Masses of the Leptons, Quarks, and Their Superpartners
	16.7 Some Other Consequences of the MSSM
	16.8 Coupling Unification in Supersymmetric GUT
	16.9 Quiz
Final Exam
Appendix A: Useful Identities
Appendix B: Solutions to Exercises
Appendix C: Solutions to Quizzes
Appendix D: Solutions to Final Exam

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