31 research outputs found
Characterization of local observables in integrable quantum field theories
Integrable quantum field theories in 1+1 dimensions have recently become
amenable to a rigorous construction, but many questions about the structure of
their local observables remain open. Our goal is to characterize these local
observables in terms of their expansion coefficients in a series expansion by
interacting annihilators and creators, similar to form factors. We establish a
rigorous one-to-one characterization, where locality of an observable is
reflected in analyticity properties of its expansion coefficients; this
includes detailed information about the high-energy behaviour of the observable
and the growth properties of the analytic functions. Our results hold for
generic observables, not only smeared pointlike fields, and the characterizing
conditions depend only on the localization region - we consider wedges and
double cones - and on the permissible high energy behaviour.Comment: minor changes, as to appear in Commun. Math. Phys.; 39 pages, 4
figures, 1 vide
Relativistische Materie in zwei Raum-Zeit-Dimensionen
Quantum field theory unifies concepts from quantum theory and from special
relativity. Its mathematically rigorous description is quite intricate and is
only partially understood; this is particularly true for the construction of
operators corresponding to measurements at a space-time point or in a bounded
space-time region. We explain this fact in simplified examples on 1+1
dimensional space-time, namely in so-called integrable models. We give a
characterization of local operators by means of the analyticity properties of
their coefficients in a certain series expansion. This also allows us to
explicitly construct examples of local operators.Comment: in German; 12 pages, 5 figures; as appeared in the proceedings of the
symposium "Raum und Materie", Villigst, October 2012; references update
Automated assessment in a programming course for mathematicians
The paper reports on a programming course for undergraduate Mathematics students in their 2nd year, with some parts compulsory for single-subject students. Assessment takes the form of several programming projects. Formative feedback as well as summative assessment is aided by automated unit tests, which allow for rapid and consistent marking, while focussing marker’s time on students who require the most help
Towards an explicit construction of local observables in integrable quantum field theories
We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh-Schlieder property, and in which sense they generate the net of algebras. Our investigation focuses on scalar models without bound states. We establish sufficient criteria for the existence of averaged fields as closable operators, and complete the construction in the specific case of the massive Ising model
Operator product expansions as a consequence of phase space properties
The paper presents a model-independent, nonperturbative proof of operator
product expansions in quantum field theory. As an input, a recently proposed
phase space condition is used that allows a precise description of point field
structures. Based on the product expansions, we also define and analyze normal
products (in the sense of Zimmermann).Comment: v3: minor wording changes, as to appear in J. Math. Phys.; 12 page