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Tangent field theory

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The modern understanding of quantum field theory underlines its effective nature: it describes only those properties of a system relevant above a certain scale. A detailed understanding of the nature of the neglected information is essential for a full application of quantum information-theoretic tools to continuum theories.

I will present an operationally motivated method for deriving an effective field theory from any microscopic description of a state. The approach is based on dimensional reduction relative to a quantum distinguishability metric. It relies on a microscopic description of experimental limitations, such as a finite spatial resolution. In this picture, the emergent field observables represent cotangent vectors on the manifold of states, and are not necessarily endowed with the full semantic of standard quantum observables.