Abstract

In physics, one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of states, and argue that the renormalization group (RG) arises from the inherent ambiguities associated with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives in a given equivalence class. This provides a unifying framework and reveals the role played by information in renormalization. We validate this idea by showing that it justifies the use of low-momenta n-point functions as statistically relevant observables around a Gaussian hypothesis. These results enable the calculation of distinguishability in quantum field theory. Our methods also provide a way to extend renormalization techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the relationships between various type of RG.

Highlights

  • Any further distribution of with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, this work must maintain attribution to the which specify representatives in a given equivalence class

  • The renormalization group (RG), as conceived by Wilson [1, 2], relies on the idea that it is possible to describe long-distance physics while essentially ignoring short-distance phenomena; Wilson argued that, if we are content with predictions to some specified accuracy, the effects of physics at smaller lengthscales can be absorbed into the values of a few parameters of some effective theory for the long-distance degrees of freedom

  • We introduced a framework which allows for the definition of effective theories in very general terms, taking into account any measure of distinguishability and any model of experimental limitations

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Summary

C Bény and T J Osborne

We think of Alice as possessing the true state of a physical system, while Bob is an experimentalist whose practical limitations are formalised by the channel. If two states ρ and ρ′ are such that (ρ) = (ρ′) they cannot be distinguished by Bob and are both just as good as hypotheses for Alice’s state This indistinguishability results in equivalence classes of states: all that Bob can hope to do is to determine in which class the true state is. When modifying a regularization parameter, as occurs in high-energy physics, or when simplifying the description of the state and isolating the relevant degrees of freedom, as commonly practised in condensed matter theory. Before we describe these two cases in more depth, we need to consider more general, and more realistic experimental limitations.

General framework
One classical mode
Classical Gaussian states
Interactions
Quantum Gaussian states
Renormalization
Distinguishability in QFT
Concluding remarks
Full Text
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