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Relativity, Particles, and Fields

Module PH2040

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2020

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022SS 2021SS 2020SS 2019SS 2018SS 2017SS 2016WS 2013/4SS 2011

Basic Information

PH2040 is a semester module in English or German language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Theory courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 90 h 10 CP

Responsible coordinator of the module PH2040 in the version of SS 2020 was Alejandro Ibarra.

Content, Learning Outcome and Preconditions


  • Special Relativity
  • The action principle
  • Canonical quantization of free fields
  • Interacting fi elds
  • Quantum Electrodynamics.


Learning Outcome

After successful completion of the module the students are able to:

  1. Understand the principles of Special Relativity and its applications.
  2. Understand the action principle and Noether's theorem in field theory.
  3. Calculate the field equations and conserved quantities from a given Lagrangian density.
  4. Quantize the free scalar field, Dirac field and electromagnetic field.
  5. Quantize systems with interacting fields.
  6. Draw Feynman diagrams and derive Feynman rules for interacting systems.
  7. Calculate scattering cross sections and decay rates in simple processes in the Yukawa theory and in quantum electrodynamics.


No requirements beyond the admission requirements for a Physics Master's degree.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Relativity, Particles, and Fields Garbrecht, B. Tue, 10:00–12:00, PH HS2
Thu, 12:00–14:00, PH HS2
UE 2 Exercise to Relativity, Particles, and Fields
Responsible/Coordination: Garbrecht, B.
dates in groups eLearning

Learning and Teaching Methods

The module consists of a lecture and exercise classes.

In the thematically structured lecture the learning content is presented. With cross references between different topics the universal concepts in physics are shown. In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In the exercise the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.


Lecture, board work, exercises in individual and group work


  • M. Peskin & D.V. Schroeder, "An Introduction to Quantum Field Theory" (Taylor & Francis)
  • S. Weinberg, "Quantum Theory of Fields (Vol.1)" (Cambridge University Press)
  • L. Ryder., "Quantum Field Theory" (Cambridge University Press) .

Module Exam

Description of exams and course work

There will be a written exam of 90 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 field equations from a given Lagrangian density.
  • Calculate the scattering cross section of the process e+e-> mu+ mu-

In the exam no learning aids are permitted.

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 passing the voluntary test exam during the semester

Exam Repetition

The exam may be repeated at the end of the semester.

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