Group of Karl Schilcher

Low Energy QCD

With the advent of precise measurements of the vector and axial-vector spectral functions, obtained from tau-lepton decay, an opportunity was opened to check the precision of the QCD sum rules in the light-quark sector of QCD and simultaneously extract some fundamental parameters of QCD. The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data. A general approach based on a functional method can be used to compare the time-like tau-data with the asymptotic space-like QCD results. This method allows one to obtain numerical results for the QCD condensates, some of the fundamental parameters of QCD.

Chiral Perturbation Theory

Recent progress in the calculation of massive Feynman integrals allows phenomenological studies of physical amplitudes to an accuracy in unison with the high precision of existing or planned experiments. Results of the two-loop calculation in full SU(3)×SU(3) chiral perturbation theory are studied for weak and electromagnetic form factors which are relevant for measurements of the kaon electromagnetic and weak charge radii, rare kaon decays and other observables of pseudoscalar mesons. Computer algebraic tools are needed to organize and simplify the required calculations.

Electrical Impedance Tomography

EIT is an imaging technique of medical diagnostics, in which one tries to obtain information on the conductivity distribution in the interior of a body by measuring currents and voltages at the surface of the body. If successfully implemented, EIT would provide a non-invasive complementary alternative to more conventional imaging techniques. We have built an electrical impedance tomograph which makes it possible to reconstruct impedance distributions in the interior of a cylinder by means of measurements of currents and potentials on its boundary. The reconstruction algorithm is based on Newton’s algorithm for the solution of non-linear integral equations, where the electric fields are calculated by the methods of finite elements and finite integrals and Green functions. The results can be represented graphically on a PC. The resolution is good enough to envisage applications in medical diagnostics such as mammography. Most previous EIT algorithms use two-dimensional models for the conductivity. Since the electric current does not flow in straight lines, this approximation seems to be unwarranted. We investigate a new approach to three-dimensional electrical impedance imaging based on a reduction of the information to be demanded from a reconstruction algorithm. Images are obtained from a single measurement by suitably simplifying the geometry of the measuring chamber and by restricting the nature of the object to be imaged and the information required from the image. In particular we seek to establish the existence or non-existence of a single object (or a small number of objects) in a homogeneous background and the location of the former in the plane defined by the measuring electrodes. Given in addition the conductivity of the object rough estimates of its position along the z-axis may be obtained.