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Table of Contents
2.7 The Electroweak Unification
3 Nuclear Forces, Meson Field Theories and Their Failures
3.1 Nuclear Forces: Observational
3.2 Yukawa Theory
3.3 Meson Field Theories and Their Failures
3.4 Experimental Discoveries of the Pions
3.5 Meson Theories Post-Pion Discovery
Part IIHeisenberg's S-matrix to String Theory
4 The S-matrix: From Heisenberg Till Now
4.1 Introduction
4.2 Kramers, Kronig and Analyticity
4.3 Connections to Causality
4.4 Causality and Analyticity in Non-relativistic Quantum Mechanics
4.5 Microcausality
5 QED: S-Matrix, Causality and Analyticity
5.1 Development of QED
5.2 Dyson Equivalence Proof
5.3 S-Matrix in QED
5.4 Causality, Analyticity, and S-Matrix in Non-perturbative RQFT
6 A Non-perturbative RQFT Primer
6.1 QFT-A Particle Perspective
6.1.1 Notations and Conventions
6.2 Quantum Fields from Particles
7 The Kallen-Lehmann Representation
7.1 Introduction
7.2 The Kallen-Lehmann Representation
7.2.1 Lessons for Analytic S-Matrix
8 The Lehmann Symanzik Zimmermann (LSZ) Formalism
8.1 The LSZ Reduction Formulae
8.1.1 The Retarded Commutator Representation
8.1.2 What if No Tricks are Used?
8.1.3 Unretarded Commutator Representation
8.1.4 Crossing Symmetry
9 Unitarity and the LSZ Formalism
9.1 Introduction
9.2 General Considerations
9.3 LSZ Formalism and Unitarity
9.3.1 Proof of Unitarity in LSZ Formalism
10 Lehmann Ellipses
10.1 Lehmann Ellipses
10.1.1 Jost-Lehmann-Dyson Theorem
11 Dispersion Relations in RQFT
11.1 Introduction
11.2 Toll's Analysis of the Logical Foundations
11.3 Dispersion Relations in QFT: General Considerations
11.4 Forward Scattering Dispersion Relations
11.4.1 Massless Particle Scattering
11.4.2 Massive Particle Scattering: Goldberger Analysis
11.4.3 Massive Particle Scattering: Symanzik Analysis
11.5 Non-forward Scattering: Salam's Approach
11.6 Fixed-t Dispersion Relations: Lehmann and Sommer
11.7 Mandelstam Double Spectral Representation
12 Some Uses and Applications of Analyticity and Dispersion Relations
12.1 Low Energy Meson-Nucleon Scattering
12.2 Pion Decay
12.3 The Froissart, Khuri-Kinoshita Bounds
12.3.1 The Pomeranchuk Theorem
12.3.2 Pi-Pi Scattering
3 Nuclear Forces, Meson Field Theories and Their Failures
3.1 Nuclear Forces: Observational
3.2 Yukawa Theory
3.3 Meson Field Theories and Their Failures
3.4 Experimental Discoveries of the Pions
3.5 Meson Theories Post-Pion Discovery
Part IIHeisenberg's S-matrix to String Theory
4 The S-matrix: From Heisenberg Till Now
4.1 Introduction
4.2 Kramers, Kronig and Analyticity
4.3 Connections to Causality
4.4 Causality and Analyticity in Non-relativistic Quantum Mechanics
4.5 Microcausality
5 QED: S-Matrix, Causality and Analyticity
5.1 Development of QED
5.2 Dyson Equivalence Proof
5.3 S-Matrix in QED
5.4 Causality, Analyticity, and S-Matrix in Non-perturbative RQFT
6 A Non-perturbative RQFT Primer
6.1 QFT-A Particle Perspective
6.1.1 Notations and Conventions
6.2 Quantum Fields from Particles
7 The Kallen-Lehmann Representation
7.1 Introduction
7.2 The Kallen-Lehmann Representation
7.2.1 Lessons for Analytic S-Matrix
8 The Lehmann Symanzik Zimmermann (LSZ) Formalism
8.1 The LSZ Reduction Formulae
8.1.1 The Retarded Commutator Representation
8.1.2 What if No Tricks are Used?
8.1.3 Unretarded Commutator Representation
8.1.4 Crossing Symmetry
9 Unitarity and the LSZ Formalism
9.1 Introduction
9.2 General Considerations
9.3 LSZ Formalism and Unitarity
9.3.1 Proof of Unitarity in LSZ Formalism
10 Lehmann Ellipses
10.1 Lehmann Ellipses
10.1.1 Jost-Lehmann-Dyson Theorem
11 Dispersion Relations in RQFT
11.1 Introduction
11.2 Toll's Analysis of the Logical Foundations
11.3 Dispersion Relations in QFT: General Considerations
11.4 Forward Scattering Dispersion Relations
11.4.1 Massless Particle Scattering
11.4.2 Massive Particle Scattering: Goldberger Analysis
11.4.3 Massive Particle Scattering: Symanzik Analysis
11.5 Non-forward Scattering: Salam's Approach
11.6 Fixed-t Dispersion Relations: Lehmann and Sommer
11.7 Mandelstam Double Spectral Representation
12 Some Uses and Applications of Analyticity and Dispersion Relations
12.1 Low Energy Meson-Nucleon Scattering
12.2 Pion Decay
12.3 The Froissart, Khuri-Kinoshita Bounds
12.3.1 The Pomeranchuk Theorem
12.3.2 Pi-Pi Scattering