2018/06/05 by Daniela Cadamuro, Cadamuro, Daniela
Mathematics · #81T05 (primary) 81T40 (secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1806.01686
openalex publication_date 2018/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The construction of pointlike fields in quantum integrable models is usually approached by constructing their n-point functions. However, convergence questions of the resulting infinite series remain unresolved even in the simplest case of the massive Ising model. On the other hand, the C*-algebraic approach to the construction considers semi-local bounded operators, but yields local operators only in a very abstract way. We use a novel approach to investigate the structure of these local observables, in the form of smeared pointlike quantum fields. Instead of considering their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with the local C*-algebras. We explicitly construct all pointlike fields of the Ising model, verify the Reeh-Schlieder property and show that they generate the local algebras by dualization.