This is a table of contents for my notes on field theory (some classical, but mostly quantum). The posts are arranged in an order that might be found in a textbook. For an alphabetical index, see this page.

These notes will be of most benefit if read in parallel with Coleman's book *Quantum Field Theory: Lectures of Sidney Coleman*.

- Hamilton's equations for relativistic fields
- Translation and rotation invariance
- Relativistic invariant integration measure
- Lorentz transformations of relativistic states
- Probability of particle outside light cone

- Harmonic oscillator to Fock space
- Lorentz transformation and translation of creation and annihilation operators

- Motivation for a quantum field theory
- Lorentz transformation and translation of explicit quantum field
- Final form for the scalar quantum field
- Free scalar field as the fundamental object
- Normal ordering

- Classical particle mechanics
- Classical field theory
- Noether's theorem in classical mechanics
- Translation symmetry and conservation of momentum
- Time translation symmetry and conservation of energy
- Rotation symmetry and conservation of angular momentum
- Noether's theorem in classical field theory
- Currents from spacetime translations and the energy-momentum tensor
- Noether's theorem and Lorentz transformations

- SchrÃ¶dinger picture
- Heisenberg picture
- Interaction picture
- Scattering and the S-matrix
- Dyson's formula and time ordering

- Wick's theorem
- Scalar fields - summary
- Wick diagrams
- Connected and disconnected Wick diagrams
- Exact solution of a one-field model
- Counterterms in interaction hamiltonians
- Ground state energy in a one-field model with static source
- Mass renormalization