Functional Derivative of the Lagrangian for a Continuous System 5. Constants of the Motion in a Simple Case 3. Conservation of the Total Momentum 5. Separation of the External Field 2. The Lagrangian in the Presence of an External Fielda. Introduction of a Lagrangian. The Lagrangian in the Coulomb Gauge.

## Photons and Atoms: Introduction to Quantum Electrodynamics by Claude Cohen-Tannoudji

The Hamiltonian in the Presence of an External Fielda. Conjugate Momenta, b. The Hamiltonian.

An Example of a Hamiltonian Different from the Energy 2. Momentum and Angular Momentum of an Arbitrary Field 6. Quantization of the Schrodinger Field 9. The General Framework 1. Fundamental Dynamical Variables. Commutation Relations 2. State Space B. Time Evolution 1. The Schrodinger Picture 2. The Heisenberg Picture. The Quantized Maxwell-Lorentz Equationsa.

## Photons and atoms: Introduction to quantum electrodynamics

The Heisenberg Equations for Particles, b. The Heisenberg Equations for Fields, c. Observables and States of the Quantized Free Field 1. Review of Various Observables of the Free Fielda. Total Energy and Total Momentum of the Field, b.

The Fields at a Given Point r of Space, c. Observables Corresponding to Photoelectric Measurements 2.

Elementary Excitations of the Quantized Free Field. Photons a. Eigenstates of the Total Energy and the Total Momentum, b. The Interpretation in Terms of Photons, c. Single-Photon States. Propagation 3. Some Properties of the Vacuuma. Qualitative Discussion, b. Mean Values and Variances of the Vacuum Field, c. Vacuum Fluctuations 4. Quasi-classical States a.

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Introducing the Quasi-classical States. Characterization of the Quasi-classical States, c. Some Properties of the Quasi-classical States, d. The Hamiltonian for the Interaction between Particles and Fields 1. Selection Rules 4. A Simple Model 2. The General Case. Quasi-classical States, c. Factored States.

### Description

Single-Photon States 3. Quasi-classical States, b. Single-Photon States, c. Two-Photon States 4. Assumptions about the Sources 2. Evolution of the Fields in the Heisenberg Picture 3.

The Schrodinger Point of View. Preliminary Calculations 2. Field Commutatorsa. Reduction of the Expressions in Terms of D. Explicit Expressions for the Commutators, c. Properties of the Commutators 3. Bose-Einstein Distribution 5. Quasi-Probabihty Densities and Characteristic Functions 6.

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Quadrature Components of a Single-Mode Field. Graphical Representation of the State of the Field 7. Squeezed States of the Radiation Field 8. Change of Gauge and of Lagrangian 2. Changes of Lagrangian and the Associated Unitary Transformationa. Changing the Lagrangian. The Two Quantum Descriptions. The Correspondence between the Two Quantum Descriptions. Application to the Electromagnetic Field 3. The General Unitary Transformation.

## Atomic and Optical Physics: Atom-photon interactions

The Lagrangian and Hamiltonian of the System 2. Simple Gauge Change; Gauge Invariancea. The New Description. The Goppert-Mayer Transformationa. The Long-Wavelength Approximation. The Advantages of the New Point of View. Generalizations 4. Motivation, b.

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Determination of the Unitary Transformation.