Hendriksen, H. (2014) Majorana particles in physics and mathematics. Bachelor's Thesis, Mathematics.
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Abstract
In 1937, the Italian physicist Ettore Majorana showed that there exist real solutions to the Dirac equation. This suggests the existence of the Majorana fermion, a neutral fermion that is equal to its antiparticle. Up until now, no Majorana fermions have been found. Recent developments in solid state physics have led to evidence that so-called Majorana zero modes can exist in superconductors. Sometimes these quasiparticles are also confusingly named "Majorana fermions". These modes or quasiparticles show some resemblance with the real Majorana fermions, however they are two completely different physical phenomena. This article mathematically describes the differences between these two concepts by the use of different Clifford algebras. For the description of the Majorana spinor a Clifford algebra is used that satisfies a pseudo-Euclidean metric, applicable in a selection of space-time dimensions. The Majorana zero mode is described by a Clifford algebra that satisfies a purely Euclidean metric in the abstract space of zero modes. Furthermore the statistics of both entities is described, where Fermi-Dirac statistics applies to the Majorana fermion and non-Abelian anyonic statistics applies to the Majorana zero modes.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:58 |
| Last Modified: | 15 Feb 2018 07:58 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/11952 |
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