## Quantum Theory of Light

Monday 8:30 - 10 am, Seminar Room 4.18

Tuesday 8:30 - 10 am, Seminar Room E04

### Content

#### 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