  This work derives the linearized equations of motion, the Lagrangian density,
the Hamiltonian density, and the canonical angular momentum density for general
perturbations [$\propto \exp(im\phi)$ with $m=0,\pm 1,..$] of a geometrically
thin self-gravitating, homentropic fluid disk including the pressure. The
theory is applied to ``eccentric,'' $m=\pm 1$ perturbations of a geometrically
thin Keplerian disk. We find $m=1$ modes at low frequencies relative to the
Keplerian frequency. Further, it shown that these modes can have negative
energy and negative angular momentum. The radial propagation of these low
frequency $m=1$ modes can transport angular momentum away from the inner region
of a disk and thus increase the rate of mass accretion. Depending on the radial
boundary conditions there can be discrete low-frequency, negative-energy, $m=1$
modes.
