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 renormalisation group 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 identifies the role played by information in renormalisation. 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 renormalisation techniques to
effective models which are not based on the usual quantum-field formalism, and
elucidates the relationships between various type of RG.

本研究发展了一种操作方法来识别状态的等价类，并且说明了重整化群的作用和信息在其中的作用，为量子场论中的区分度计算提供了一种方法。同时，本文也为不基于传统量子场理论的有效模型扩展重整化技术提供了途径，并阐明了不同类型重整化群之间的关系。