The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

Rational design of selective anion receptors

The new family of the anion receptors based on oligoureas with varied flexibility was developed and studied. The preparation of the urea chains containing two different units in various sequences was elaborated. The complete sets of four cyclic trimers and six tetramers based on the two units were prepared. Their conformational and complexation properties were studied with NMR spectroscopy and X-ray structure determinations, their behaviour towards various anions was evaluated and compared. The synthesis and the same studies were performed also with four different cyclic hexamers. During these studies the remarkable templation by two halide anions was observed.