Course Code : | 2001WETKVT |

Study domain: | Physics |

Academic year: | 2019-2020 |

Semester: | 2nd semester |

Contact hours: | 45 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | English |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Jacques Tempere Alexander Sevrin |

At the start of this course the student should have acquired the following competences:

specific prerequisites for this course

- general knowledge of the use of a PC and the Internet

specific prerequisites for this course

Theoretical physics, in particular: quantum mechanics, electromagnetism and classical field theory.

- The student understands quantum field theory, and can explain the theory and its main concepts (propagator, Feynman diagrams and Feynman rules,...) and illustrate his/her explanation with examples.
- The student can apply quantum field theory to problems in many-body physics, such as the many-electron system and the interacting Bose gas.
- The student can apply quantum field theory to calculate scattering cross-sections.
- The student can propose and develop models in the framework of quantum field theory and understand the lowest order implications of these models.

We start with a general introduction and reminder on classical field theory. This is studied with a number of simple examples in mind, such as scalar bosons and massive vector bosons. We also look at gauge fields, symmetries, conserved currents, coordinate transforms and component transforms in the framework of classical field theory. The electromagnetism of charged scalar bosons is investigated as an example of a gauge theory.

Next, we make the transition from classical to quantum field theory. For this purpose we focus on the path integral (Lagrangian) formalism - this is complementary to the Hamiltonian formalism investigated in the course of solid state physics 2. We derive the propagator and interpret it (as greens function, and as a description of particles as quanta of excitations of a field). We investigate how classical and quantum fields differ. This difference is particularly striking for fermionic fields where we have to introduce Grassmann variables. We first study quantum field theory for exactly solvable models.

Then we switch to interacting fields .These are no longer exactly solvable, and we introduce the perturbative technique of Feynman diagrams. Problems of convergence (and solutions with regularization and renormalization) are discussed. Next, we turn to quantum statistical field theory, necessary to study fields at finite temperature. The free energy is calculated as a function of temperature, using the technique of Matsubara summations. In this part we use the phi^4 theory as textbook example.

Finally, we apply the techniques to quantum electrodynamics. For this theory we focus on how to calculate scattering amplitudes and the S-matrix.

The course has an international dimension.

Besides three spatial dimensions and one temporal dimension, this course also has six international dimensions. However, these are compactified into Calabi-Yau spaces and are unreachable for the matter sector of the course. Nevertheless, students are generally encouraged to send gravitons into the international dimensions.

Class contact teachingLectures Practice sessions

Personal workAssignments Individually

**5.3 Facilities for working students ***

Directed self-study (possibly with response lecture)

Personal work

Directed self-study (possibly with response lecture)

- Blended learning with limited amount of classroom activities in the evening

ExaminationWritten examination without oral presentation Written with oral presentation Open book

Continuous assessmentExercises Assignments

Continuous assessment

Your own notes that you take during the seminars, and the course syllabus.

Anthony Zee, Quantum Field Theory in a Nutshell - 2nd Edition (Princeton University Press, 2010).

Franz Mandl, Graham Shaw, Quantum Field Theory - 2nd Edition (Wiley VCH, 2010).

W. Greiner and J. Reinhardt, Field Quantization (Springer-Verlag, 1996).

Naoto Nagaosa, Quantum Field Theory in Condensed Matter Physics (Springer-Verlag Berlin, 2009).

Prof.dr. Jacques Tempere

Lokaal N.017, gebouw N

Campus Drie Eiken

tel: 03 / 265 2866