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Revolving around Noether's Theorem

Borghols, B.H.G. (2016) Revolving around Noether's Theorem. Bachelor's Thesis, Physics.

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This thesis explores the possibilities and difficulties that arise within mathematics and physics as a result of Noether’s first theorem, which roughly says that symmetries of a La- grangian imply conservation laws. In the mathematical part of this thesis, we investigate how to find symmetries of a functional (Lagrangian) or differential equations (Euler-Lagrange) in the first place. Two different methods, the first in the framework of point geometry and the second in the framework of infinite jet spaces, to find symmetries in a systematic way are discussed. In the physics part of the thesis, we will look at Noether’s theorem in the context of Quantum Field Theory: Goldstone’s theorem states that spontaneously broken continuous symmetries correspond to massless modes called Nambu-Goldstone bosons. We will look at some qualitative and quantitative aspects of these bosons. This theory is then extended to encapsulate the possibility of ‘broken’ translational symmetry. We look at two ways in which the translational symmetry may be broken: discrete rather than continuous translational symmetry, and local rather than global symmetry. It turns out that in both cases, the symmetry breaking may affect the number of Nambu-Goldstone bosons and in the latter case their qualitative properties.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Physics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:14
Last Modified: 15 Feb 2018 08:14

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