  In a local Fermi liquid (LFL), we show that there is a line of weak first
order phase transitions between the ferromagnetic and paramagnetic phases due
to purely quantum fluctuations. We predict that an instability towards
superconductivity is only possible in the ferromagnetic state. At T=0 we find a
point on the phase diagram where all three phases meet and we call this a
quantum triple point (QTP). A simple application of the Gibbs phase rule shows
that only these three phases can meet at the QTP. This provides a natural
explanation of the absence of superconductivity at this point coming from the
paramagnetic side of the phase diagram, as observed in the recently discovered
ferromagnetic superconductor, $UGe_{2}$.
