Isospectral deformations of the Dirac operator

We give more details about an integrable system in which the Dirac operator D=d+d^* on a finite simple graph G or Riemannian manifold M is deformed using a Hamiltonian system D'=[B,h(D)] with B=d-d^* + i b. The deformed operator D(t) = d(t) + b(t) + d(t)^* defines a new exterior derivative d(t) and a new Dirac operator C(t) = d(t) + d(t)^* and Laplacian M(t) = d(t) d(t)^* + d(t)* d(t) and so a new distance on G or a new metric on M.Comment: 32 pages, 8 figure

A Modular and Flexible Architecture for an Integrated Corpus Query System

The paper describes the architecture of an integrated and extensible corpus query system developed at the University of Stuttgart and gives examples of some of the modules realized within this architecture. The modules form the core of a corpus workbench. Within the proposed architecture, information required for the evaluation of queries may be derived from different knowledge sources (the corpus text, databases, on-line thesauri) and by different means: either through direct lookup in a database or by calling external tools which may infer the necessary information at the time of query evaluation. The information available and the method of information access can be stated declaratively and individually for each corpus, leading to a flexible, extensible and modular corpus workbench.Comment: 10 pages, uuencoded gzip'ped PostScript; presented at COMPLEX'9

Natural renormalization

A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration constants differential renormalization is most closely related to the theory of generalized functions. The special properties of this scheme are illustrated by application to the toy example of a free massive bosonic theory. Then we apply the scheme to the phi^4-theory. The two-point function is calculated up to five loops. The renormalization group is analyzed, the beta-function and the anomalous dimension are calculated up to fourth and fifth order, respectively.Comment: 23 pages, LaTeX, AMSsymbols, epsf style, 3 PostScript figure