Equivalence of dimensional reduction and dimensional regularisation

For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional regularisation (DREG), to all orders in perturbation theory and for a general renormalisable theory. The two regularisation schemes are related by an analytic redefinition of the couplings, under which the -functions calculated using DRED transform into those computed in DREG. TheS-matrix calculated using DRED is numerically equal to the DREG version, ensuring that both schemes give the same physics.     

Design and Asymmetric Synthesis of beta-Strand Peptidomimetics

We describe the asymmetric synthesis of non-peptidic compounds that feature rigid backbone conformations and present various side-chain functions. The key step in the synthesis of these compounds is the C-acylation of an appropriate ketone with a suitably protected aspartic acid derivative. The resulting dipeptide modules may be connected to form tetrapeptide mimics. Specifically is described the mimicry of a four-residue segment of CD4, the cellular receptor of HIV-1. The design was based on molecular modeling and the X-ray crystal structures of CD4 and intended to present the most important side chains and backbone elements of the Phe43-Lys46 segment.     

Extensions of automorphisms and gauge symmetries

We characterize the automorphisms of aC ^*-algebra which extend to automorphisms of the crossed product by a compact group dual. The case where the inclusion is equipped with a group of automorphisms commuting with the dual action is also treated. These results are applied to the analysis of broken gauge symmetries in Quantum Field Theory to draw conclusions on the structure of the degenerate vacua on the field algebra.Dedicated to Huzihiro ArakiResearch supported by MURST and CNR, GNAFA