Avatars of Margulis invariants and proper actions

In this article, we interpret affine Anosov representations of any word hyperbolic group in $\mathsf{SO}_0(n-1,n)\ltimes\mathbb{R}^{2n-1}$ as infinitesimal versions of representations of word hyperbolic groups in $\mathsf{SO}_0(n,n)$ which are both Anosov in $\mathsf{SO}_0(n,n)$ with respect to the stabilizer of an oriented $(n-1)$-dimensional isotropic plane and Anosov in $\mathsf{SL}(2n,\mathbb{R})$ with respect to the stabilizer of an oriented $n$-dimensional plane. Moreover, we show that representations of word hyperbolic groups in $\mathsf{SO}_0(n,n)$ which are Anosov in $\mathsf{SO}_0(n,n)$ with respect to the stabilizer of an oriented $(n-1)$-dimensional isotropic plane, are Anosov in $\mathsf{SL}(2n,\mathbb{R})$ with respect to the stabilizer of an oriented $n$-dimensional plane if and only if its action on $\mathsf{SO}_0(n,n)/\mathsf{SO}_0(n-1,n)$ is proper. In the process, we also provide various different interpretations of the Margulis invariant.Comment: 40 page

Analysis of ω\omega 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 $\omega$ 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 $\omega$ in a thermal gas of mesons, baryons and anti-baryons in equilibrium for several values of temperature and baryon chemical potential