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- A note on emergent classical behavior and approximations to decoherence functionals

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13110085

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

superspace.

©2012 Institut Périmètre de Physique Théorique