- 1. Introduction
- 2. Some rules for sum rules
- 2.1. Causality and analyticity
- 2.2. Derivation of dispersion relations
- 2.3. Crossing symmetry
- 2.4. Unitarity
- 2.5. Low-energy theorems and sum rules
- 2.6. Relaxing the convergence condition
- 2.7. Divergencies, subtractions, and renormalization
- 2.8. An approximate sum rule for the proton charge
- 3. The Kramers-Kronig relation
- 3.1. Refraction in a relativistic medium
- 3.2. The low-frequency limit : the Lorentz-Lorenz relation
- 3.3. CMB refraction index
- 4. Sum rules for Compton scattering
- 4.1. Forward kinematics : helicity amplitudes for any spin
- 4.2. Optical theorem : dispersion relation
- 4.3. Low-energy expansion and sum rules
- 4.4. Empirical evaluations for the nucleon
- 5. Virtual Compton scattering and quasi-real sum rules
- 5.1. VVCS and structure functions
- 5.2. Elastic versus Born contributions
- 5.3. The Burkhardt-Cottingham sum rule
- 5.4. The Schwinger sum rule
- 5.5. Generalized Baldin sum rules
- 5.6. Longitudinal amplitude : to subtract or unsubtract?
- 5.7. The Bernabéu-Tarrach sum rule
- 5.8. Validation in the parton model
- 5.9. Further spin-dependent relations
- 6. Sum rules for light-by-light scattering
- 6.1. Compton scattering off a photon
- 6.2. Symmetries, unitarity, and dispersion relations
- 6.3. Effective field theorems
- 6.4. The sum rules
- 6.5. Perturbative verification
- 6.6. Non-perturbative verification : bound state
- 6.7. Implications for mesons
- 6.8. Composite Higgs
- 7. Virtual light-by-light scattering
- 7.1. Forward scattering amplitudes
- 7.2. Sum rules in perturbation theory
- 8. Compton-scattering sum rules for vector bosons
- 8.1. Electromagnetic moments : natural values
- 8.2. Gauge symmetries and spin degrees of freedom
- 8.3. Tree-level unitarity : GDH sum rule
- 8.4. Forward VVCS and virtual LbL scattering
- 9. Vacuum polarization and g - 2 of the muon
- 9.1. Vacuum polarization in QED
- 9.2. Unitarity and sum rules
- 9.3. Introduction to the muon anomaly
- 9.4. Hadronic vacuum polarization in the muon anomaly
- 9.5. Muon anomaly via the Schwinger sum rule
- 10. Dispersion theory of hydrogen-like atoms
- 10.1. Quantum-mechanical Coulomb problem
- 10.2. One-photon exchange in dispersive representation
- 10.3. Vacuum polarization contributions to the Lamb shift
- 10.4. Finite-size effects
- 10.5. Two-photon exchange and polarizability effects
- 10.6. Radiative corrections
- 10.7. Proton self-energy and the charge-radius definition.
Causality: Cause and effect. In classical physics, an effect cannot occur before its cause. In Einstein's theory of special relativity, causality means that an effect cannot occur from a cause that is not in the back (past) light cone of that event. The books cover the useful physical relations inferred by unitarity and causality. A famous example is the Kramers-Kronig relation for the refractive index of a gas or dilute medium. For example, chapter 3 generalises the Kramers-Kronig relation to relativistic medium, such as CMB (photon gas). These relations are extensively also used in particle and nuclear physics. Especially useful are the so-called 'sum rules', such as the Gerasimov-Drell-Hearn (GDH) or the Baldin sum rule. The author notes that the first edition is too brief. In his teaching practice, he sees that it is challenging to use as a standalone text. He intends to improve the explanations of many topics that students found particularly challenging. The additional material will make the book more timely, self-contained, and logically complete.