  To make sense of quantum field theory in an arbitrary (globally hyperbolic)
curved spacetime, the theory must be formulated in a local and covariant manner
in terms of locally measureable field observables. Since a generic curved
spacetime does not possess symmetries or a unique notion of a vacuum state, the
theory also must be formulated in a manner that does not require symmetries or
a preferred notion of a ``vacuum state'' and ``particles''. We propose such a
formulation of quantum field theory, wherein the operator product expansion
(OPE) of the quantum fields is elevated to a fundamental status, and the
quantum field theory is viewed as being defined by its OPE. Since the OPE
coefficients may be better behaved than any quantities having to do with
states, we suggest that it may be possible to perturbatively construct the OPE
coefficients--and, thus, the quantum field theory. By contrast, ground/vacuum
states--in spacetimes, such as Minkowski spacetime, where they may be
defined--cannot vary analytically with the parameters of the theory. We argue
that this implies that composite fields may acquire nonvanishing vacuum state
expectation values due to nonperturbative effects. We speculate that this could
account for the existence of a nonvanishing vacuum expectation value of the
stress-energy tensor of a quantum field occurring at a scale much smaller than
the natural scales of the theory.
