Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/121903
Title: Lie groups and algebras in particle physics
Author: Fraxanet Morales, Joana
Director/Tutor: Costa Farràs, Laura
Keywords: Grups de Lie
Treballs de fi de grau
Àlgebres de Lie
Representacions d'àlgebres
Partícules (Física nuclear)
Lie groups
Bachelor's thesis
Lie algebras
Representations of algebras
Particles (Nuclear physics)
Issue Date: 28-Jun-2017
Abstract: [en] The present document is a first introduction to the Theory of Lie Groups and Lie Algebras and their representations. Lie Groups verify the characteristics of both a group and a smooth manifold structure. They arise from the need to study continuous symmetries, which is exactly what is needed for some branches of modern Theoretical Physics and in particular for quantum mechanics. The main objectives of this work are the following. First of all, to introduce the notion of a matrix Lie Group and see some examples, which will lead us to the general notion of Lie Group. From there, we will define the exponential map, which is the link to the notion of Lie Algebras. Every matrix Lie Group comes attached somehow to its Lie Algebra. Next we will introduce some notions of Representation Theory. Using the detailed examples of SU(2) and SU(3), we will study how the irreducible representations of certain types of Lie Groups are constructed through their Lie Algebras. Finally, we will state a general classification for the irreducible representations of the complex semisimple Lie Algebras.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Laura Costa Farràs
URI: http://hdl.handle.net/2445/121903
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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