Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Spin-Restricted Coupled-Cluster-Theorie fuer offenschalige Zustaende

Spin-Restricted Coupled-Cluster-Theorie fuer offenschaligeZustaende Die Berechnung von Energien und Eigenschaften offenschaligerAtome undMolekuele mit Hilfe der hochgenauenCoupled-Cluster-(CC)-Theoriewar bisher mit einem - im Vergleich zur BerechnunggeschlossenschaligerZustaende - erhoehten Rechenaufwand und der sogenannten'Spinkontamination' behaftet. Um diesen Problemenentgegenzuwirken,stellten P.G.Szalay und J.Gauss die 'Spin-RestrictedCoupled-Cluster-Theorie' vor. Im Rahmen dieser Arbeit wird die urspruenglich aufDublett-Zustaendebeschraenkte Theorie so verallgemeinert, dass jederbeliebige Spinzustandmit einem einheitlichen Satz von Gleichungen beschriebenwerden kann. Dadie Moller-Plesset-(MP)-Stoerungstheorie bei der BerechnungoffenschaligerZustaende mit aehnlichen Problemen behaftet ist, wirddarueberhinaus dieSpin-Restricted-(SR)-MP-Stoerungstheorie zweiter und dritterOrdnungeingefuehrt. Um Molekueleigenschaften berechnen zu koennen,werdenanalytische Ableitungen der Energie sowohl fuer den SR-CC-als auch denSR-MP-Ansatz hergeleitet. Bei den folgenden Testrechnungenstellt sichheraus, dass sowohl SR-CC- als auch SR-MP-Ansaetze diegleiche Genauigkeitbieten wie konventionelle CC- und MP-Ansaetze. Dabei sinddieSpinerwartungswerte der SR-CC-Wellenfunktionen identisch mitdem exaktenWert. Im Rahmen der Testrechnungen stellt sich heraus, dassder SR-CC-Ansatz nicht 'size-konsistent', der numerische Fehler abervernachlaessigbar klein ist. Abschliessend werden dieHintergruende derfehlenden 'Size-Konsistenz' diskutiert.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Analysis of the influence of epitope flanking regions on MHC class I restricted antigen presentation

Peptides presented by MHC class I molecules for CTL recognition are derived mainly from cytosolic proteins. For antigen presentation on the cell surface, epitopes require correct processing by cytosolic and ER proteases, efficient TAP transport and MHC class I binding affinity. The efficiency of epitope generation depends not only on the epitope itself, but also on its flanking regions. In this project, the influence of the C-terminal region of the model epitope SIINFEKL (S8L) from chicken ovalbumin (aa 257-264) on antigen processing has been investigated. S8L is a well characterized epitope presented on the murine MHC class I molecule, H-2Kb. The Flp-In 293Kb cell line was transfected with different constructs each enabling the expression of the S8L sequence with different defined C-terminal flanking regions. The constructs differed at the two first C-terminal positions after the S8L epitope, so called P1’ and P2’. At these sites, all 20 amino acids were exchanged consecutively and tested for their influence on H-2Kb/S8L presentation on the cell surface of the Flp-In 293Kb cells. The detection of this complex was performed by immunostaining and flow cytometry. The prevailing assumption is that proteasomal cleavages are exclusively responsible for the generation of the final C-termini of CTL epitopes. Nevertheless, recent publications showed that TPPII (tripeptidyl peptidase II) is required for the generation of the correct C-terminus of the HLA-A3-restricted HIV epitope Nef(73-82). With this background, the dependence of the S8L generation on proteasomal cleavage of the designed constructs was characterized using proteasomal inhibitors. The results obtained indicate that it is crucial for proteasomal cleavage, which amino acid is flanking the C-terminus of an epitope. Furthermore, partially proteasome independent S8L generation from specific S8L-precursor peptides was observed. Hence, the possibility of other existing endo- or carboxy-peptidases in the cytosol that could be involved in the correct trimming of the C-terminus of antigenic peptides for MHC class I presentation was investigated, performing specific knockdowns and using inhibitors against the target peptidases. In parallel, a purification strategy to identify the novel peptidase was established. The purified peaks showing an endopeptidase activity were further analyzed by mass spectrometry and some potential peptidases (like e.g. Lon) were identified, which have to be further characterized.