  We consider generating functionals for computing correlators in quantum field
theories with random potentials. Examples of such theories include condensed
matter systems with quenched disorder (e.g. spin glass) or cosmological systems
in context of the string theory landscape (e.g. cosmic inflation). We use the
so-called replica trick to define two different generating functionals for
calculating correlators of the quantum fields averaged over a given
distribution of random potentials. The first generating functional is
appropriate for calculating averaged (in-out) amplitudes and involves a single
replica of fields, but the replica limit is taken to an (unphysical) negative
one number of fields outside of the path integral. When the number of replicas
is doubled the generating functional can also be used for calculating averaged
probabilities (squared amplitudes) using the in-in construction. The second
generating functional involves an infinite number of replicas, but can be used
for calculating both in-out and in-in correlators and the replica limits are
taken to only a zero number of fields. We discuss the formalism in details for
a single real scalar field, but the generalization to more fields or to
different types of fields is straightforward. We work out three examples: one
where the mass of scalar field is treated as a random variable and two where
the functional form of interactions is random, one described by a Gaussian
random field and the other by a Euclidean action in the field configuration
space.
