Quantum Field Theory

• Basic Concepts of Quantum Field Theory
• Path integral representation of quantum field theory, perturbation expansion, Feynman diagrams
• From Green functions to scattering cross sections, particle states, LSZ reduction
• Renormalization, regularization, effective field theory, renormalization group, running couplings
• Symmetries and relativistic particles & quantum fields with spin, fermionic path integral, Feynman rules for general fields
• Vector fields and gauge symmetry, quantum electrodynamics

After successful completion of the module the students are able to

• to compute Green functions in perturbation theory, including loop corrections, and apply these to calculations of high-energy reactions;
• to quantise non-Abelian gauge theory and to calculate tree- and loop processes;
• to understand the concepts of regularisation and renormalisation and to apply these in calculations;
• to improve perturbative calculations using the renormalisation group;
• to construct effective quantum field theories.

No preconditions in addition to the requirements for the Master’s program in Physics. Very helpful is an introductory lecture like “Relativity, particles, fields”. More information on the course at https://www.groups.ph.tum.de/t75/teaching/ws21-quantum-field-theory-tum-and-tmp/

Lecture, blackboard presentation; homework problems and their discussion in tutorial groups

The lecture is designed for the presentation of the subject, usually by blackboard presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problems, which cover important aspects of the field. The homework problems should develop the analytic skills of the students and their ability to perform calculations. The homework problems are discussed by the students themselves under the supervision of a tutor in order to develop the skills to solve and explain a physics problem coherently.

Blackboard, possibly supplemented with slides. Homework problems for deepening and practising the learned topics

• Peskin & Schroeder, "An Introduction to Quantum Field Theory"
• Weinberg, "Quantum Theory of Fields"
• Schwartz, "Quantum Field Theory and the Standard Model"

There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Calculate the Feynmanrules of a QFT with Scalar, Fermion or Vector fields and determine the leading contribution to the scattering cross-section of a 2->2 process.
• Calculate a 1-loop diagram, regularize and renormalize
• Integrate out a heavy particle and determine the resulting effective field theory
• Determine the Noether-current and the Ward Identities of a QFT with scalar fields in the fundamental of SO(3)
• Calculate the beta function and determine its behavior.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of

• 1. preparing at least 50% of the exercises on the exercise sheets,
• 2. presenting at least three exercises at the blackboard,
• 3. participtating actively in the tutorials.