The connection between QFT and random fields

Peter Morgan; Yale University, Department of Physics

Abstract: The connection between classical mechanics and quantum mechanics has historically been dominated by quantization and, in the opposite direction, the correspondence principle and Ehrenfest's theorem, which fall far short of the clarity of isomorphisms between mathematical structures.  In contrast, we can use Koopman's Hilbert space formalism for classical mechanics to construct isomorphisms between classical and quantum Hilbert spaces and between classical and quantum algebras of operators, which allows a unified approach to joint and incompatible measurements.  With a common measurement theory in place, other differences between classical and quantum can be more clearly described.  At the level of field theories, signal analysis can be adopted as an empiricist way to unify QFT and random fields, which allows a carefully judged classical intuition to suggest several ways to rethink QFT.

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