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Ribosomal RNA genes (rDNA) exist in yeast both as a single chromosomal array of tandemly repeated units and as extrachromosomal units named 3um plasmids, although the relationship between these two forms is unclear. Inheritance of rDNA was studied using two systems. The first used a naturally occuring rDNA restriction enzyme polymorphism between two strains to distinguish between their rDNA arrays, and the second involved cloning a tRNA suppressor gene into rDNA to label individual rDNA units. An added interest to the study of the inheritance of rDNA in yeast was the possible association between it and the inheritance of the Psi factor, an enigmatic type of nonsense suppressor in yeast which shows extra-chromosomal inheritance. In a cross heterozygous for the rDNA polymorphism and the psi factor, tetrad analysis suggested that the psi factor had segregated 4:0. The majority of the rDNA units segregated in a 2:2 fashion, which suggested that reciprocal recombination in the rDNA of psi⁺ diploids is heavily suppressed as was previously shown for psi^- diploids. A heterologous plasmid containing the tRNA suppressor gene was constructed and transformed into haploid and diploid hosts. A series of transformants was obtained and physical and genetic analysis suggested that they contained tRNA suppressor gene(s) integrated into their rDNA. In a cross heterozygous for rDNA-tRNA gene insert(s), 6% of the tetrads dissected showed a meiotic segregation of the suppressed phenotype which could most probably be accounted for by inter-chromosomal gene conversion. This observation could be interpreted in two ways. Firstly, recombination intermediates between rDNA on homologues may occur in meiosis, but they are mostly resolved as gene conversions without reciprocal cross-over. Alternatively, gene conversion tracts in rDNA are rare but very long so that the tRNA gene insert was always included in the event. 3um rDNA plasmids containing the tRNA gene marker were not detected in any of the transformants analysed. An extensive quantitative analysis of the rate of reversion of the suppressed phenotype amongst these transformants identified a particulary unstable transformant group. It was proposed that the mechanism of reversion was loss of the tRNA gene insert by unequal sisterstrand exchange, and the mechanism was shown to be independent of the recombination/repair genes RAD1, RAD52, and RAD51. A genetic analysis of stability suggested that there may have been at least two loci segregating in the host strains with additive effects on stability.

We study the relations among unitarity cuts of a Feynman integral computed via diagrammatic cutting rules, the discontinuity across the corresponding branch cut, and the coproduct of the integral. For single unitarity cuts, these relations are familiar, and we show that they can be generalized to cuts in internal masses and sequences of cuts in different channels and/or internal masses. We develop techniques for computing the cuts of Feynman integrals in real kinematics. Using concrete one- and two-loop scalar integral examples we demonstrate that it is possible to reconstruct a Feynman integral from either single or double unitarity cuts. We then formulate a new set of complex kinematics cutting rules generalising the ones defined in real kinematics, which allows us to define and compute cuts of general one-loop graphs, with any number of cut propagators. With these rules, which are consistent with the complex kinematic cuts used in the framework of generalised unitarity, we can describe more of the analytic structure of Feynman diagrams. We use them to compute new results for maximal cuts of box diagrams with different mass configurations as well as the maximal cut of the massless pentagon. Finally, we construct a purely graphical coproduct of one-loop scalar Feynman diagrams. In this construction, the only ingredients are the diagram under consideration, the diagrams obtained by contracting some of its propagators, and the diagram itself with some of its propagators cut. Using our new definition of cut, we map the graphical coproduct to the coproduct acting on the functions Feynman diagrams and their cuts evaluate to. We finish by examining the consequences of the graphical coproduct in the study of discontinuities and differential equations of Feynman integrals.

archives@tulane.edu / In this work, five algorithms of negative dimensional integration (NDIM) are compared in several examples of Feynman diagram calculations, and the resulting solutions are compared. The methods used are the Ricotta method without parametrization, the Ricotta method with Schwinger parametrization, the Suzuki method, the Anastasiou method, and the method of brackets. It is found that for one-loop diagrams, the method of brackets gives the same solution as the other methods, but without requiring analytic continuation of the gamma factors in the solution. For multi-loop diagrams, the method of brackets gives solutions in a simpler form than the other methods, and often gives fewer possible solutions as well. In addition to its use in the evaluation of Feynman diagrams, the method of brackets is also useful when extended to the evaluation of definite integrals over the positive real numbers. This extended method of brackets is applied to several examples of definite integrals, and the five NDIM methods are also used to evaluate these examples when possible. In particular, it is shown that the method of brackets is the only method of NDIM which may be extended to the evaluation of a large class of definite integrals over the positive real numbers. / 1 / Kristina E. VanDusen

A computer program that symbolically generates and evaluates all Feynman diagrams required for scattering amplitude for exclusive processes is tested, corrected, extended, and brought to operational status. The sensitivity of perturbative QCD predictions for the nucleon form factors, ψ → pp̅, and 𝛾𝛾 → pp̅, to the theoretical uncertainties of the nucleon wave function and the form of the running coupling constant is investigated. A new prediction for the cross-section for 𝛾𝛾 → Δ++ Δ̅++ with sum-rule wave functions is presented. As a product of the development of the computer program, the quark amplitudes for meson-baryon scattering are obtained. Integrations of the quark amplitudes over wave functions are carried out by cutting off singularities. The numerical reliability of the integration and its sensitivity to the cut-off’s and the choice of wave function are investigated. / Ph. D. / incomplete_metadata

Yung Man Hong = 受歐姆阻尼振子和光學系統內的彼德曼因數及費曼圖展開 / 翁文康. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 95-99). / Text in English; abstracts in English and Chinese. / Yung Man Hong = Shou ou mu zu ni zhen zi he guang xue xi tong nei de Bideman yin shu ji Feiman tu zhan kai / Weng Wenkang. / Acknowledgement --- p.iii / Chapter 1 --- Overview --- p.1 / Chapter 1.1 --- The Langevin Equation --- p.1 / Chapter 1.2 --- Excess Noise in Lasers --- p.4 / Chapter 1.3 --- Non-orthogonality --- p.9 / Chapter 2 --- Bilinear Map and Eigenvector Expansion --- p.12 / Chapter 2.1 --- Introduction --- p.12 / Chapter 2.2 --- Mathematical Formalism --- p.14 / Chapter 2.3 --- Criticality and Divergence --- p.19 / Chapter 2.4 --- Perturbations and Cancellations --- p.25 / Chapter 3 --- Generalized Petermann Factor --- p.34 / Chapter 3.1 --- Introduction --- p.34 / Chapter 3.2 --- Petermann Factor in Optical Systems --- p.36 / Chapter 3.3 --- Generalized Petermann Factor --- p.41 / Chapter 3.4 --- Thermal Correlation Functions --- p.43 / Chapter 3.5 --- Fluctuation-Dissipation Theorem --- p.46 / Chapter 3.6 --- Weak Damping versus Near-Degeneracy --- p.49 / Chapter 4 --- Continuum Generalization --- p.56 / Chapter 4.1 --- Bilinear map --- p.56 / Chapter 4.2 --- Critical Points --- p.58 / Chapter 4.3 --- Semiclassical Laser Theory --- p.63 / Chapter 5 --- Diagrammatic Expansions --- p.71 / Chapter 5.1 --- Introduction --- p.71 / Chapter 5.2 --- Nonlinearly Coupled Oscillators --- p.72 / Chapter 5.3 --- Path Integral Method --- p.76 / Chapter 5.4 --- Feynman Diagram --- p.81 / Chapter 6 --- Conclusion --- p.87 / Chapter A --- Derivation of the Langevin equation --- p.89

In the work described in this thesis, the Feynman-Dyson perturbation theory, developed from quantum field theory, was employed in semiempirical calculations on trans - polyacetylene. A variety of soliton-like excited states of the molecule were studied by the PPP-UHF-RPA method. The results of this study provide useful information on the nature of these states, which are thought to account for the unique electrical conduction properties of trans - polyacetylene and similar conducting polymers. Feynman-Dyson perturbation theory was also used to extend Hartree-Fock theory by the inclusion of time-independent second-order self-energy insertions. The results of calculations on polyenes show that consideration of this approach is warranted, as the contribution of the second- order terms is significant. The computer program, written during the course of the research reported here, is discussed as well. / Ph. D.

With the use of chiral theory of mesons [1], [2] we evaluate the decay rate of η′ → π+π−π+π−. Our theoretical study of this problem is different from the previous theo- retical study [3] and our predicted result is in a good agreement with the experiment. In this chiral theory we evaluate Feynman diagrams up to one loop and the decay rate is calculated with the use of triangle and box diagrams. The ρ0 meson includes in both type of diagrams as a resonance state. Divergent integrals in the loop calculations are regularized with the use of n-dimensional ’t Hooft-Veltman regularization technique. At the last step to obtain the decay rate, the phase space integral has been calculated.

We calculate tree-level scattering amplitudes in φ^3 theory and Yang-Mills theory by means of the perturbiner expansion. This involves solving the Euler-Lagrange equations of motion perturbatively via a multi-particle ansatz, and using Berends-Giele recursion relations to extract the solution from simple on-shell data. The results are Berends-Giele currents which are then used to calculate the scattering amplitudes. The theoretical calculations are implemented into a Mathematica script which effectively handles recursive calculations and allows us to calculate amplitudes for an arbitrary number of particles.

In order to find quantum corrections to the de Sitter entropy, a new approach to higher loop Feynman integral computations on the sphere is presented. Arbitrary scalar Feynman integrals on a spherical background are brought into the generalized Euler integral (A-hypergeometric series/GKZ systems) form by expressing the massive scalar propagator as a bivariate radial Mellin transform of the massless scalar propagator in one higher dimensional Euclidean flat space. This formulation is expanded to include massive and massless vector fields by construction of similar embedding space propagators. Vector Feynman integrals are shown to be sums over generalized Euler integral formed of underlying scalar Feynman integrals. Granting existence of general spin embedding space propagators, general spin Feynman integrals are shown, by the construction of a "master" integral, to also be sums over generalized Euler integral representations of scalar Feynman integrals. Finding exact embedding space propagator expressions for fields of integer spin ≥ 2 and half integer spin is left to future work.