  The Entropic Dynamics reconstruction of quantum mechanics is extended to
quantum field theory in curved space-time. The Entropic Dynamics framework,
which derives quantum theory as an application of the method of maximum
entropy, is combined with the covariant methods of Dirac, Hojman, Kucha\v{r},
and Teitelboim, which they used to develop a framework for classical covariant
Hamiltonian theories. The goal is to formulate an information-based alternative
to current approaches based on algebraic quantum field theory. One key
ingredient is the adoption of a local notion of entropic time in which instants
are defined on curved three-dimensional surfaces and time evolution consists of
the accumulation of changes induced by local deformations of these surfaces.
The resulting dynamics is a non-dissipative diffusion that is constrained by
the requirements of foliation invariance and incorporates the necessary local
quantum potentials. As applications of the formalism we derive the Ehrenfest
relations for fields in curved-spacetime and briefly discuss the nature of
divergences in quantum field theory.
