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Avatars of Margulis invariants and proper actions
In this article, we interpret affine Anosov representations of any word
hyperbolic group in as
infinitesimal versions of representations of word hyperbolic groups in
which are both Anosov in with respect
to the stabilizer of an oriented -dimensional isotropic plane and Anosov
in with respect to the stabilizer of an oriented
-dimensional plane. Moreover, we show that representations of word
hyperbolic groups in which are Anosov in
with respect to the stabilizer of an oriented
-dimensional isotropic plane, are Anosov in
with respect to the stabilizer of an oriented -dimensional plane if and only
if its action on is proper. In the
process, we also provide various different interpretations of the Margulis
invariant.Comment: 40 page
Analysis of self-energy at finite temperature and density in the real-time formalism
Using the real time formalism of field theory at finite temperature and
density we have evaluated the in-medium self-energy from baryon and
meson loops. We have analyzed in detail the discontinuities across the branch
cuts of the self-energy function and obtained the imaginary part from the
non-vanishing contributions in the cut regions. An extensive set of resonances
have been considered in the baryon loops. Adding the meson loop contribution we
obtain the full modified spectral function of in a thermal gas of
mesons, baryons and anti-baryons in equilibrium for several values of
temperature and baryon chemical potential
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