arXiv subjects

Henning Bostelmann

Publications and source records attributed to Henning Bostelmann.

23 records · Page 2Linked to original sources

arXiv2008

On dilation symmetries arising from scaling limits

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.

math-ph↗

arXiv2008

Scaling algebras and pointlike fields: A nonperturbative approach to renormalization

We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.

math-ph↗

arXiv2005

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).

math-ph↗

arXiv2005

Phase space properties and the short distance structure in quantum field theory

The paper investigates relations between the phase space structure of a quantum field theory ("nuclearity") and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that allows a very detailed description of the theory's field content. An appendix discusses noninteracting models as examples.

math-ph↗

arXiv2005

Statistical analysis of quality measures for mobile ad hoc networks

How can the quality of a mobile ad hoc network (MANET) be quantified? This work aims at an answer based on the lower network layers, i.e. on connectivity between the wireless nodes, using statistical methods. A number of different quality measures are introduced and classified according to their scaling behaviour. They are analysed in a statistical model of a 1-dimensional MANET system (corresponding e.g. to cars on a road). Neglecting boundary effects, the model turns out to be exactly solvable, so that explicit analytical results for the quality levels can be obtained both at fixed system size and in the limit of large systems. In particular, this improves estimates known in the literature for the probability of connectedness of 1-dimensional MANETs.

cs.NI↗