Quantum field theory (QFT) is a common framework in many branches of physics, exhibiting an unexpected unity in the description of elementary quantum processes that deeply modified our view of physical reality. Many of the key results of QFT are obtained through a perturbative expansion, but there are crucial areas of applications that do not rely on it. The aim of the course is to provide a view of some results in these areas, with examples both in elementary particle and condensed matter physics, emphasizing the underlying common features.
Examples are only outlined, but not discussed in detail and in the following program are between brackets. Some topics in the program might be alternative, depending on the interests and knowledge of the students.
Proposed program
1) Reconstruction theorem: What precisely a QFT is, how one can reconstruct quantum fields out of correlation functions, how they are related to experiments.
2) Quantum solitons: kinks (phi4, polyacetilene), vortices (Higgs model, superconductors), monopoles (Dirac, t’Hooft-Polyakov, spin ice), and their role in the phase transitions.
3) Anomalies: chiral anomaly (the eta mass problem in QCD) and parity anomaly (topological insulators, graphene).
Examples are only outlined, but not discussed in detail and in the following program are between brackets. Some topics in the program might be alternative, depending on the interests and knowledge of the students.
Proposed program
1) Reconstruction theorem: What precisely a QFT is, how one can reconstruct quantum fields out of correlation functions, how they are related to experiments.
2) Quantum solitons: kinks (phi4, polyacetilene), vortices (Higgs model, superconductors), monopoles (Dirac, t’Hooft-Polyakov, spin ice), and their role in the phase transitions.
3) Anomalies: chiral anomaly (the eta mass problem in QCD) and parity anomaly (topological insulators, graphene).
- Docente: Pieralberto Marchetti