I studied theoretical physics at the Faculty of Mathematics and Physics of the
Charles University in Prague. In those early years, I was rather mathematically inclined. See my
diploma thesis (in Czech!) on a Hopf-algebraic theory of
renormalization, which I defended in 2002 under the supervision of Professor J. Niederle. Since then I have worked at the Nuclear Physics Institute of the Academy of Sciences of the
Czech Republic. Thanks to the broad interests of my advisor, Dr J. Hošek, I touched a number of topics, ranging from dynamical electroweak symmetry breaking to general
properties of spontaneous symmetry breaking in nonrelativistic systems. My humble attempts to understand some of the related problems are summarized in the doctoral thesis which I defended in June 2006.
Starting in 2007, I spent more than three years at the Institute for
Theoretical Physics, Goethe University in Frankfurt am Main as a member of the dense matter group. Since October 2010 I have been a postdoc with the theoretical high energy physics
group of the Bielefeld University. Even though I try to keep working on diverse topics, essentially all my activities can be summarized by the keywords spontaneous
symmetry breaking and quantum many-body (especially relativistic) systems at finite temperature and density. If you are interested in more details, have a look at
my list of publications.
Quantum Mechanics lectures at
the Bielefeld University
The following links refer to my old classes on quantum mechanics and quantum field theory at the Charles University (MFF) and the Czech Technical University (FJFI) in Prague. All
these pages are in Czech!
I guess everyone (well, perhaps at least physicists, maybe just theorists ... anyway, I hope I am not the only one) has faced the situation that they wanted to do some simple
calculation including all factors such as 2π correct, and did not have their favorite textbook with the necessary formulas at hand. Moreover, each book usually makes use of a slightly
different notation, which may be quite annoying when one needs to combine several sources. With this motivation, I started as a PhD student to write down my own set of potentially useful formulas
so that I did not have to rely on literature. I have also added a few more detailed pieces of text on miscellaneous topics. Don't expect any big science, this is all simple textbook material, but
hopefully someone might find it useful.
(pdf) Some basic notes on differential geometry of surfaces in Euclidean space.
(pdf) How to calculate traces of differential operators: method of (covariant) symbols.
(pdf) Notes on the LOFF phase in imbalanced superconductors.
(pdf) Some more advanced loop integrals as well as finite-temperature sum-integrals using dimensional
regularization. Only integrals that I checked and/or used myself are included; much more complete lists are available in literature.
(pdf) Algebra of block matrices and the basic formulas of the Nambu-Gorkov formalism; derivation of the
Grassmann integral on the Nambu space.
(pdf) Derivation of the Haar measure for unitary groups.
(pdf) Details on fitting parameters in the two-flavor NJL model using various regularization schemes. (Just for practitioners; if
you don't know what NJL model is, ignore this.)
(pdf) Notes on the BCS theory and the derivation of the Ginzburg-Landau functional.
(pdf) General theory of Fierz transformations with explicit expressions for the Fierz coefficients of the
Lorentz algebra in both the particle-antiparticle and particle-particle channels (including Lorentz-violating, rotationally-covariant fermion bilinears).
(pdf) Cross sections and decay rates; basic formulas.
(pdf) Loop integrals using Feynman parameterization; explicit expressions for the divergent and
finite parts of the integrals in dimensional as well as cutoff regularization.
(pdf) Algebra of Dirac gamma matrices; most standard and some less standard formulas.
Fakultät für Physik
E-mail: tbrauner at physik dot uni-bielefeld dot de