My work on Gauge
Field Theories
After completing my studies I
decided to write
my diploma thesis in the Department of Relativistic Physics at
Jena University. The thesis dealt with symmetries of
electromagnetic fields. As a result, I got a complete
classification of highly symmetric (4-6 Killing vectors =
independent symmetries) electromagnetic fields.
This was just the time when
non-Abelian gauge
fields became very popular with the theoretical and later
experimental success of the Salam-Weinberg theory of electro-weak
interactions. Although I'm no longer actively working in this
field, I still believe that the unification of electromagnetic and
weak interactions was one of the greatest revolutions of 20th
century physics.
This
way I extended my former work on
symmetries of classical fields to non-Abelian gauge fields in my
PhD thesis which I completed in 1984. With non-Abelian gauge
fields, one has to take into account the gauge freedom: Consider
a simple example: For being symmetric, the potential of a gauge
field after rotation need not to be identical to the one before
rotation; instead, it is sufficient that the two agree up to a
gauge transformation. This idea was not originally mine, but
based on it I made an extensive classification of highly
symmetric Abelian U(1) as well as non-Abelian SU(2) gauge fields
integrating a lot of previously known solutions. A summarizing
report on this work can be found in J. Phys. A 18
(1985), 3087-3100.
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Online since: 1997
Latest
Update: 01/04/2007