- can compute simple quantum-mechanical path integrals
- understands the origin of the perturbative expansion for scalar field theory and its relation with Feynman diagrams
- compute correlation functions from Feynman diagrams or in canonical quantization
- masters the canonical quantization of the free scalar field, and can solve the Dirac equation and canonically quantize free fermions
- is familiar with Grassmann algebra and can compute fermionic path integrals, can apply Feynman rules and compute simple scattering amplitudes in QED
- understands the concepts of regularization and renormalization and can apply them in simple examples
Quantum field theories emerged from the confluence of quantum mechanics and special relativity, and provide an amazingly accurate theoretical framework for describing the behaviour of subatomic particles and forces. This course will give an introduction into quantum field theory, both conceptually and technically. Canonical and covariant quantization methods will be discussed, with an emphasis on the path integral formulation, which finds manifold applications in both particle physics and condensed matter systems. Topics covered include the quantum-mechanical path integral, the quantization of bosonic and fermionic fields, functional techniques involving generating functionals and correlators, and perturbation theory in terms of Feynman diagrams.