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A note on emergent classical behavior and approximations to decoherence functionals

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Although it can only
be argued to have become consequential in the study of quantum cosmology, the
question ``Why do we observe a classical world? " has been one of the
biggest preoccupations of quantum foundations. In the consistent
histories formalism, the question is shifted to an analysis of
the telltale sign of quantum mechanics: superposition of states. In
the consistent histories formalism, histories of the system which
``decohere", i.e. fall out of superposition or have negligible
interference can be subjected to a notion of classical probability. In
this paper we use an extension of Kirchoff's diffraction formula for wave
functions on configuration spaces to give a different analysis and an
approximation of decoherence. The Kirchoff diffraction formula lies
conveniently at the midway between path integrals, wave equations, and
classical behavior. By using it, we formulate an approximate dampening of
the amplitude of superposition of histories. The dampening acts on each
middle element of the fine-grained history {c_\alpha}, and is a function of the
angle formed between {c_{n-1},c_n} and {c_n,c_{n+1}}, as classical
trajectories in configuration space. As an example we apply the formalism
to a modified gravity theory in the ADM gravitational conformal