  We perform a microscropic analysis of how the constraints imposed by
conservation laws affect $q=0$ Pomeranchuk instabilities in a Fermi liquid. The
conventional view is that these instabilities are determined by the static
interaction between low-energy quasiparticles near the Fermi surface, in the
limit of vanishing momentum transfer $q$. The condition for a Pomeranchuk
instability is set by $F^{c(s)}_l =-1$, where $F^{c(s)}_l$ (a Landau parameter)
is a properly normalized partial component of the anti-symmetrized static
interaction $F(k,k+q; p,p-q)$ in a charge (c) or spin (s) sub-channel with
angular momentum $l$. However, it is known that conservation laws for total
spin and charge prevent Pomeranchuk instabilities for $l=1$ spin- and charge-
current order parameters. Our study aims to understand whether this holds only
for these special forms of $l=1$ order parameters, or is a more generic result.
To this end we perform a diagrammatic analysis of spin and charge
susceptibilities for charge and spin density order parameters, as well as
perturbative calculations to second order in the Hubbard $U$. We argue that for
$l=1$ spin-current and charge-current order parameters, certain vertex
functions, which are determined by high-energy fermions, vanish at
$F^{c(s)}_{l=1}=-1$, preventing a Pomeranchuk instability from taking place.
For an order parameter with a generic $l=1$ form-factor, the vertex function is
not expressed in terms of $F^{c(s)}_{l=1}$, and a Pomeranchuk instability does
occur when $F^{c(s)}_1=-1$. We argue that for other values of $l$, a
Pomeranchuk instability occurs at $F^{c(s)}_{l} =-1$ for an order parameter
with any form-factor
