math-ph — Mathematical Physics

Ghosts in Poisson Brane Gases

Contributed by Deep Bhattacharjee, Ushashi Bhattacharya

A Poisson gas of branes with mass intensity $\nu$ dresses the graviton propagator by the random entire function $\prod_k(1+p^2/t_k)$. We prove that the gas average of the propagator equals $p^{-2}\exp[-\int p^2\nu(\dd t)/(p^2+t)]$, so that the massive states carry total weight $e^{-\nu(0,\infty)}-1<0$. For $\nu=\lambda(t)\,\dd t/t$ the averaged spectrum consists of ghosts alone exactly when $\lambda\le1$, and every average with a finite four-dimensional tadpole has states of both signs. Frozen gases keep alternating residues.