The aim of this thesis is to examine the hard $S$-matrix for QED and QCD, due to Hannesdottir and Schwartz [1], both recreating known results, and finding new results in lower dimensions. Electrons by themselves are not gauge invariant, and in the massless limit do not give finite $S$-matrix elements for individual processes; one needs to add together seemingly arbitrary combinations of diagrams in order to be able to calculate the scattering cross-section. One remedy is to exchange the bare electron for a dressed state, or equivalently to include the dressing in the $S$-matrix itself. This gives rise to a formalism in which one needs only consider time cuts of an individual diagram in order to find finite $S$-matrix elements. The main result of this thesis is the examination of the results which are found by Hannesdottir and Schwartz in a model system of fewer dimensions. This may be of use for toy model calculations in QCD, where 2+1-dimensional QED better models certain phenomena than does 3+1-dimensional QED.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kau-95233 |
| Date | January 2023 |
| Creators | Savinainen, David |
| Publisher | Karlstads universitet, Institutionen för ingenjörsvetenskap och fysik (from 2013) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf, application/pdf |
| Rights | info:eu-repo/semantics/openAccess, info:eu-repo/semantics/openAccess |
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