2014/02/28 by Cédric Bény, Tobias J. Osborne, Tobias J Osborne · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Equivalence (formal languages) #Gaussian #Measure (data warehouse) #Observable #Quantum #Quantum many-body systems #Renormalization #Renormalization group #Statistical inference #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1088/1367-2630/17/8/083005
published as New J. Phys. 17 (2015) 083005 · This version corrects an error at the end of Section V: the adjoint map R does not simply factor over modes
arxiv created 2015/07/28 · openalex publication_date 2015/08/05 · arxiv updated 2015/08/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.