-
Every Monday, 08:15-10:00 (lecture) and 10:15-12:00 (exercises)
in old lecture hall 2, 1.22 (Physics Institute).
Content:
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 "Symmetries, Particles and Fields" 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:
Symmetries
- Spacetime symmetries: the (homogeneous/inhomogeneous (proper orthochronous)) Lorentz group
- Representation theory of the most important physical symmetry groups ( SO(3), SU(2), SO+(3,1), ...)
- Importance of relativistic spacetime symmetry for the quantum mechanical formalism
(e.g. in the construction of field equations)
- Mathematical aspects of relativistic (quantum) field theories
- Fock space formalism (bosons/fermions)
Methods
- Distribution theory
- Field quantization: field operators as operator-valued distributions
- Gauge fixing, gauge invariance and causality at the classical and quantum level
- Possibly ghost fields
- UV divergences
- Interactions & cross sections: perturbative calculations
For time reasons, of course, not all of the above topics can be treated.
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 15
September 22
September 29
October 6: lecture will probably be cancelled
October 13
October 20
October 27
November 3
November 10
November 17: lecture will probably be cancelled
November 24
December 1
December 8
December 15: final exam
Exercise sheets:
|
Created April 2025 by Andreas Aste.