Moltmaker, Wout (2020) A Hopf algebra approach to q-Deformation of Physics. Bachelor's Thesis, Mathematics.
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Abstract
In this thesis we study the theory of Hopf algebras and their applications to q-deformation of physics. As an example of q-deformation we study the q-deformed quantum harmonic oscillator. We develop the basic theory of Hopf algebras, and generalize this to Hopf algebra objects in arbitrary braided categories. We also discuss the representation theory of Hopf algebras and their connections to algebraic topology; in particular braid- and knot theory. As applications we derive knot invariants from several particular Hopf algebras, and we demonstrate a Tannaka-Krein duality for Hopf algebras. We then discuss the systematic q-deformation of basic physics, including an explicit description of q-deformed Minkowski spacetime. Finally, we discuss the consequences of such a q-deformation for models of physics. This includes a dicussion of basic q-deformed field theories on q-Minkowski spacetime.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Roest, D. and Veen, van der, R.I. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 27 Jul 2020 13:30 |
| Last Modified: | 27 Jul 2020 13:30 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/22693 |
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