  It has been widely assumed that partially quenched chiral perturbation theory
is the correct low-energy effective theory for partially quenched QCD. Here we
present arguments supporting this assumption. First, we show that, for
partially quenched QCD with staggered quarks, a transfer matrix can be
constructed. This transfer matrix is not Hermitian, but it is bounded, and it
can be used to construct correlation functions in the usual way. Combining
these observations with an extension of the Vafa--Witten theorem to the
partially quenched theory allows us to argue that the partially quenched theory
satisfies the cluster property. By extending Leutwyler's analysis of the
unquenched case to the partially quenched theory, we then conclude that the
existence and properties of the transfer matrix as well as clustering are
sufficient for partially quenched chiral perturbation theory to be the correct
low-energy theory for partially quenched QCD.
