<p>Godkänd; 1994; 20070410 (ysko)</p>

No description available.

No description available.

This thesis reviews the theory of group extensions, gerbes and twisted K-theory. Application to anomalies in gauge theory is briefly discussed. The main results are presented in two appended scientific papers. In the first paper we establish, by construction, a criterion for when an infinite dimensional abelian Lie algebra extension corresponds to a Lie group extension. In the second paper we introduce the fractional loop group L_qG, construct highest weight modules for the Lie algebra and discuss an application to twisted K-theory on G. / QC 20101111

The Yang-Mills gauge theories play prominent role in modern high energy physics and the direct non-perturbative calculations present the main challenge in the field.Two dimensional gauge theories provide a nice playground where it is possible to carry out exact computations and at the same time some non-trivial phenomena canbe studied. This thesis is devoted to review and summarize a core portion of the quantum version of this field, accompanying the reader through the technicalities that one can encounter during the first approach to the subject.The thesis starts with a brief introduction to the subject and a brief review of the literature, the first two chapters are then spent on the computation of the partition functions over the simplest surfaces, i.e. disk and cylinder, using different formalisms.In chapter 4 there is presented the generalization of the procedure in order to find the general partition function that can be applied over any orientable surface (not necessarily closed). Interesting observables in this theory are the so called Wilson loops, chapter 5 contains the definition and a presentation of the non-intersecting ones over closed surfaces. In the end some of these encountered formulae have been applied to U(1) and SU(N) groups, i.e. we derived some partition functions of Maxwell theory and quantum chromodynamics over non-trivial surfaces and we gave the tools to explore more complex cases. The appendices contain one a brief review of the mathematics, the other all the step by step computations performed during the proofs.

In this project, we compute the Hagedorn temperature in N=4 supersymmetric Yang-Mills theory and in pure Yang-Mills theory by determining the temperature at which the partition function becomes non-analytic. The gauge group is taken to be either SU(N) or O(N) in the large N limit. We derive the partition function with combinatorics, counting the single-trace operators (and thereby the gauge invariant states) allowed by the theory. Then we determine the single-particle partition functions associated with fermions, bosons, and gluons, whose contributions make up the full partition function. These single-particle functions are derived independently using two different approaches (both producing the same result), where the first method relies on the state-operator correspondence of conformal field theories, and the second relies on the spin representations of the particles. We also derive the partition function on a compact space by integrating over the gauge group manifold. By using random matrix theory and standard large N methods, the integral simplifies. The resulting Hagedorn temperature matches that derived from combinatorics. We compute the precise temperature in two theories.

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Syftet med detta arbete är att försöka komma fram till hur elever som läser tekniskt och naturvetenskapligt program på gymnasiet uppfattar ämnet fysik. En enkät ligger till grund för undersökningen. Enligt eleverna blir ämnet tråkigt när det är för mycket teori och muntlig undervisning. Däremot blir ämnet intressantare när eleverna får ägna sig åt laborationer och experiment. En viktig faktor för både undervisningen och trivseln i klassrummet är läraren. Resultatet av undervisningen påverkas också positivt om eleverna har roligt när de undervisas. Överlag är fysikämnet intressant enligt eleverna och det finns ett tydligt intresse för att få förståelse för olika fenomen samtidigt som flertalet elever ser valet av gymnasieprogram som en framtidsinvestering.

Bristande kompetensnivå när studenterna når mer avancerade kurser inom optik tyder på att universitetet har ett problem i upplägget av detta ämne. Denna studie djupdyker in i den första optikkursen som ges på Uppsala Universitet, “Vågor och Optik” för Fysikkandidater och Civilingenjörer i vissa program. Genom att delta på laborationer, analysera kursutvärderingar och uppgifter som ges under kursens gång kan tydliga problem identifieras och bland annat ge en insikt i studenternas eget perspektiv på kursen.  För att sedan åtgärda dessa problem undersöks ett antal alternativa sätt att bedriva undervisningen med ett speciellt intresse av digitala hjälpmedel då denna studie bidrar med en vetenskaplig grund till ett parallellt projekt att utveckla en pedagogisk app för att ytterligare förbättra utbildningen. Studien avslutas sedan med sju steg för att förbättra kursen genom att åtgärda de problem som identifierats i kursen.

The aim of this report is to introduce the reader to the field of integrability in classical and quantum physics. The report begins with a reminder of Hamiltonian mechanics and explains the notion of Liouville integrability. The introduction of the Lax formalism is then used to show a method for generating conserved quantities that lends itself well to a generalisation to classical field theory. In this context, the fundamental concepts of r-matrix, monodromy and transfer matrix are presented. To close the section on classical integrability, the classical inverse scattering method is presented on the example of the Korteweg - de Vries equation. Solving the spin chain XXX 1/2 using the coordinate Bethe ansatz is then used to open the door to the field of quantum integrability. The generalisation of the classical concepts introduced previously to the quantum domain will allow us to implement the algebraic Bethe ansatz method, which is a more general approach. Using this procedure, the examples of the spin chains XXX s and XXZ s are treated, clearly highlighting the importance of symmetries in the field of integrability. Finally, a brief overview of the Gauge/Bethe correspondence is presented.