Modular Nuclearity and Localization

Modular Nuclearity: A Generally Covariant Perspective

A quantum field theory in its algebraic description may admit many irregular states. So far, selection criteria to distinguish physically reasonable states have been restricted to free fields (Hadamard condition) or to flat spacetimes (e.g., Buchholz-Wichmann nuclearity). We propose instead to use a modular `p-condition, which is an extension of a strengthened modular nuclearity condition to ge...

Pd-η 3-C6H9 complexes of the Trost modular ligand: high nuclearity columnar aggregation controlled by concentration, solvent and counterion† †Electronic supplementary information (ESI) available: Synthesis and Characterisation of compounds, and full details of aggregation studies by NMR, SANS, and MM3. See DOI: 10.1039/c5sc01181g Click here for additional data file.

Construction of Quantum Field Theories with Factorizing S-Matrices

A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields which are localized in infinitely extended, wedge-shaped regions of Minkowski space are constructed explicitly. In the second step, local observables are analyz...

Nuclearity of Hankel operators for ultradifferentiable control systems

Nuclearity of the Hankel operator is a known sufficient condition for convergence of Lyapunov-balanced truncations. We show how a previous result on nuclearity of Hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class D with p ≥ 1 (the case p = 1 being the analytic case). For semigroups that are generated by a Dunford-Schwartz spectral operat...

Approximation property and nuclearity on mixed-norm Lp, modulation and Wiener amalgam spaces

In this paper, we first prove the metric approximation property for weighted mixed-norm L (p1,...,pn) w spaces. Using Gabor frame representation, this implies that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck’s theory becomes applicable, and we give criteria for nuclearity and r-nuclearity for operators acting on these spaces as well a...