- Part I. Classical Fields
- 1. Variational Calculus
- 2. Semi-riemannian geometry
- Part II. Quantum Mechanics
- 1. The postulates of quantum mechanics
- 1. The geometry of projective Hilbert spaces
- 2. Quantum mechanical symmetries
- 2. Deformation quantization
- 1. Fedosov's construction of star-products
- 3. Quantum spin systems
- 1. The quasi-local algebra of a spin lattice model
- 4. Molecular quantum mechanics
- 1. The von Neumann--Wigner no crossing-rule
- Part III. Quantum Fields
- 1. Representations of the Lorentz and Poincare groups
- 1. The Lorentz invariant measure on a mass hyperboloid
- 2. Axiomatic quantum field theory a la Wightman and Garding
- 1. Wightman axioms
- 2. Fock space
- 3. The free scalar field
- 3. Axiomatic quantum field theory a la Haag--Kastler