One of my major interests is the description of particle interactions in dense matter using field theoretic, quantum kinetic, and thermodynamic methods, and in applications of these methods to astroparticle physics and cosmology. By doing this, we can investigate the influence of particle properties such as neutrino masses on various astrophysical scenarios and derive constraints on such properties by comparing with observations.

For example, in my PhD thesis I developed a new
**field theoretic formulation**
of neutrino oscillations in dense matter which unifies neutrino
refraction with non-forward scattering causing
oscillation "damping". This **fully
relativistic approach**
includes antineutrino degrees of freedom and leads to a kinetic
description by a "non-abelian" Boltzmann-like equation for the
neutrino and antineutrino density matrices. It accounts for
non-linear effects such as neutrino refraction
due to self-interactions and Pauli-blocking of mixed
neutrino final states. This quantum kinetic formalism
can also be applied to other mixing phenomena such as
polarization of the microwave background in the ambient
plasma, and even to the quantum mechanical measurement problem.

Using the formalism discussed above, **Georg Raffelt**, **Leo
Stodolsky** (
Max-Planck-Institut für Physik, München),
Hans-Thomas Janka (Max
Planck Institut für Astrophysik), Steen Hannestad
(University of Aarhus) and I calculated the time scale of neutrino flavor
conversion in a supernova core as a function of neutrino mixing
angles and masses (see
recent paper).
This conversion can influence the transport properties of the
neutrino gas and thus supernova evolution.
By numerical simulations of the full non-linear kinetic
equations, I also investigated flavor conversion
outside the core where neutrino self-interactions are important.
This resulted in a more reliable determination of the
neutrino mixing parameter range which would render r-process
nucleosynthesis in supernovae impossible. These bounds lie
in a mass range where neutrinos could serve as hot dark matter
and are thus cosmologically important.

Together with **Michael Turner** (U of C), I developed a simple
**analytical
transport formalism for weakly interacting
particles** which can also be unstable. By applying it to
supernova observations, we derived bounds on mass and lifetime of
the tau-neutrino that complement experimental constraints.

Recently, I derived a new
**sum rule for the nucleon spin density
structure function of hot nuclear matter** which
allows improved estimates of the rather
poorly known weak interaction rates in dense
nuclear matter. This has important implications for the cooling
history of a supernova and its neutrino signal, and for
astrophysical bounds on the
properties of certain hypothetical particles such as axions. It
shows that weak interactions are not strongly suppressed in hot,
dense nuclear matter compared to the "naive" lowest order rates
which result from treating the medium constituents as free
particles. In a rather large collaboration with **Wolfgang Keil**,
**Thomas Janka** (MPA, Garching), **David Schramm,**,
Michael Turner (U of C), and **John Ellis**
(CERN),
we have recently incorporated this new assessment of weak
interaction rates in hot nuclear matter into a numerical supernova
simulation. As a result, we showed that
**
supernova bounds on
the axion mass** are relaxed by about a factor of 2.

In contrast to the density structure function, the nucleon spin
density structure function has a finite width which is related
to the spin fluctuation rate of individual nucleons. This
implies a new mode of
**energy transfer between neutrinos and the nuclear
medium** which is of comparable importance to ordinary recoil
effects. In addition, weak interaction rates depend on spatial
correlations of the nuclear spin- and isospin-densities. Thus,
accurate measurements of the neutrino signal from a nearby
supernova might provide important information on the equation of
state of hot nuclear matter. Such measurements might be possible
with the next generation neutrino detectors such as
Super-Kamiokande
which just started operation or the Sudbury
Neutrino Observatory which is under construction.
Motivated by that, I plan to extend these investigations and do a
systematic study of weak interaction rates in nuclear matter
using methods of finite temperature field theory. My goal is
to treat the temporal and the usually much more familiar
spatial dependence of the structure functions on an equal footing
for the first time. I believe that this will allow considerable
progress in the understanding of the type II supernova phenomenon.

As a first step in this direction, here is a simple
**
toy model for nucleon spin evolution in a hot
and dense nuclear medium** I developed with Georg Raffelt.
A given nucleon is limited to
one-dimensional motion in a distribution of external, spin-dependent
scattering potentials. The figure on the left is an example for
the numerically calculated spin autocorrelation function
in frequency space at a temperature of 30 MeV, where the
external potential varies
between 10 and 30 MeV, depending on the relative orientation
of external and test particle spin. The density of scatterers
for the cases shown is 0.2, 0.4, 0.8, 1.2, 2, 4, and 12
per femtometer in descending order at the left end.

For all plausible parameter combinations mimicking the conditions in a supernova core, the width of the spin density structure function was found to be less than the temperature. This is in contrast with a naive perturbative calculation based on the one-pion exchange potential which overestimates this width and suggests a large suppression of the neutrino opacities by nucleon spin fluctuations.

I am now thinking about a more ambitious calculation of
response functions in hot nuclear matter, using quantum
Monte Carlo codes that implement realistic nuclear interactions
in a truly many body frame work. This work is planned
together with **Ted Ressell** (U of C).

I am performing the theoretical studies mostly in connection
with the **
Sonderforschungsbereich Astroteilchenphysik (particle astrophysics)
**. To combine such studies with full blown numerical supernova
simulations, I collaborate with people from the
**hydrodynamics group** at the
Max Planck Institut
für Astrophysik, Garching bei München, such as
Thomas Janka who is an expert in computational
astrophysics.