2008/12/27 by Henning Bostelmann, Claudio D'Antoni, Claudio D’Antoni +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Covariance #Dilation (metric space) #Geometry #Homogeneous space #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Observable #Physics #Quantum field theory #Quantum mechanics #Scaling #Scaling limit #Statistical physics #Symmetry (geometry) #Theoretical physics #math-ph #math.MP #msc:46L45 #msc:81T05
paper · pdf · doi:10.1007/s00220-009-0899-9
published as Commun.Math.Phys.294:21-60,2010 · 40 pages, 1 figure
arxiv created 2008/12/27 · openalex publication_date 2009/08/29 · arxiv updated 2013/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum field theories, at short scales, can be approximated by a scaling limit theory. In this approximation, an additional symmetry is gained, namely dilation covariance. To understand the structure of this dilation symmetry, we investigate it in a nonperturbative, model independent context. To that end, it turns out to be necessary to consider non-pure vacuum states in the limit. These can be decomposed into an integral of pure states; we investigate how the symmetries and observables of the theory behave under this decomposition. In particular, we consider several natural conditions of increasing strength that yield restrictions on the decomposed dilation symmetry.