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Symmetries of the Point Particle
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

We study point particles to illustrate the various symmetries such as the Poincaré group and its non-relativistic version. In order to find the Noether charges and the Noether currents, which are conserved under physical symmetries, we study Noether’s theorem. We describe the Pauli-Lubanski spin vector, which is invariant under the Poincaré group and describes the spin of a particle in field theory. By promoting the Pauli-Lubanski spin vector to an operator in the quantized theory we will see that it describes the spin of a particle. Moreover, we find an action for a smooth spinning bosonic particle by compactifying one string dimension together with one embedding dimension. As with the Pauli-Lubanski spin vector, we need to quantize this action to confirm that it is the action for a smooth spinning particle.

Abstract [sv]

Vi studerar punktpartiklar för att illustrera olika symemtrier som t.ex. Poincaré gruppen och dess icke-relativistiska version. För att hitta de Noether laddningar och Noether strömmar, vilka är bevarade under symmetrier, studerar vi Noether’s sats. Vi beskriver Pauli-Lubanksi spin vektorn, vilken har en invarians under Poincaré gruppen och beskriver spin hos en partikel i fältteori. Genom att låta Pauli-Lubanski spin vektorn agera på ett tillstånd i kvantfältteori ser vi att den beskriver spin hos en partikel. Dessutom finner vi en verkan för en spinnande partikel genom att kompaktifiera en bosonisk sträng dimension tillsammans med en inbäddad dimension. Som med Pauli-Lubanski spin vektorn, kvantiserar vi denna verkan för att bekräfta att det är en verkan för en spinnande partikel.

Place, publisher, year, edition, pages
2014. , 34 p.
Keyword [en]
symmetries, spin, classical physics, classical field theory, action, smooth spinning particle, pauli-lubanski, noether, theorem, poincare group, lorentz group, galilean transformations, relativistic, equations of motion, boost, rotation, translation, quantization, bosonic string, rigid particle, momentum, momenta, generators
National Category
Other Physics Topics Physical Sciences
URN: urn:nbn:se:uu:diva-227338OAI: oai:DiVA.org:uu-227338DiVA: diva2:728883
Educational program
Bachelor Programme in Physics
Available from: 2014-08-15 Created: 2014-06-25 Last updated: 2014-08-15Bibliographically approved

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