Quantum Theory of Light

Monday 8:30 - 10 am, Seminar Room 4.18
Tuesday 8:30 - 10 am, Seminar Room E04


I. Classical Fields

I.1 Discrete mechanical systems
I.2 Continuum mechanical systems
I.3 Classical scalar fields
I.4 Lagrangian density for the electromagnetic field

II The Classical Electromagnetic Field

II.1 The pure radiation filed: electromagnetic field as the superposition of the plane waves
II.2 The energy of the electromagnetic field in vacuum as the sum of energies of oscillators
II.3 Density of states of the electromagnetic field
II.4 Hamiltonian of a charge in the electromagnetic field: Lorentz force
II.5 General system of particles and fields: Hamiltonian in the Coulomb gauge

III The Quantum Electromagnetic Field

III.1 Resume: Hamiltonian for the classical electromagnetic field in free space
III.2 Second quantization
III.3 Photon states
III.4 Quantized radiation field
III.5 Commutation relations
III.6 Properties of photons
III.7 The quantum vacuum
III.8 Quantum states of radiation: Fock, coherent and squeezed states. The standard quantum limit
III.9 Further remarks on vacuum fluctuations; the classical limit

IV Photons and Atoms

IV.1 Preliminary considerations: A charge in the presence of a classical vector potential. Aharonov-Bohm effect
IV.2 Photons and atoms. The Hamiltonian in Coulomb gauge
IV.3 Radiative instability of the excited state. Fermi golden rule
IV.4 The self-energy of a bound electron: the Lamb shift
IV.5 Scattering processes: scattering of photons by atomic electrons
IV.6 Some mathematical tools

V The Resolvent: Nonperturbative Calculation of Transition Amplitudes

V.1 Green functions and propagators
V.2 Resolvent of the Hamiltonian
V.3 Typical approximations in atomic physics (1st part)
V.4 Examples: Decay of an excited state. Spectral distribution of the emitted photons.
V.5 Validity of the approximations (2nd part)

VI Spontaneous Emission by a System of Two Neighboring Atoms