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Every Monday, 08:15-10:00 (lecture) and 10:15-12:00 (exercises)
in old lecture hall 2, 1.22 (Physics Institute).
Content:
- Brief introduction to special relativity (notation and conventions)
- Fundamental symmetries as the guiding principle of modern physics
- Groups, Lie groups, and Lie algebras
- Representations of the rotation and Lorentz groups
- Relativistic field theory: Weyl, Dirac, Majorana fields, and related concepts
- Selected mathematical aspects of relativistic (quantum) field theories
The quantization of a classical particle leads to the
concept of the wave function –
but what happens when wave functions themselves are quantized?
Relativistic quantum field theories,
as they appear for example in the Standard Model of particle physics,
describe nature demonstrably successfully down to length scales
of the order of
10-19 m = 10-10 nm and are the language with which high-energy processes
at accelerators
such as the LHC at CERN can be described.
An important tool in the description of physical theories,
whether quantized or not,
is the concept of symmetry.
In physics, a symmetry is a transformation of an object of our
perception,
which preserves properties
of the object. The corresponding object may be either
a physical system or
a mathematical structure (e.g. a law of nature).
Symmetries of an object’s property naturally form a transformation group.
The understanding of spacetime symmetries, representable with the help of the
Poincaré or Lorentz group
SO+(3,1),
first enables the definition of the particle concept in physics, and
internal (gauge) symmetries
such as SU(3) in QCD are indispensable mathematical concepts when
the structure of
the fundamental interactions in modern theories
is to be described.
My annually offered lecture "Mathematical Methods in Particle Physics" addresses various aspects
of fundamental topics such as the group and representation theory of the most important physical
symmetry groups and their consequences for the formalisms (field equations, interaction terms)
in relativistic particle physics, and the mathematical techniques
for describing relativistic elementary particle processes.
Of course, in the limited time frame only a selection of the topics listed below
can be covered:
The following mathematical definitions and concepts should be familiar to the listener
from linear algebra:
Basic algebraic notions.
Current parts of a script will be distributed in the lecture.
Lecture notes (continuously updated)
Suggested literature
Planned lecture and exercise dates:
September 14
September 21
September 28
October 5: no lecture
October 12
October 19
October 26
November 2
November 9
November 16
November 23
November 30
December 7
December 14: final exam
Exercise sheets:
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Created August 2026 by Andreas Aste.