faculteit: "FNWI" en publicatiejaar: "2011"
| Auteur||Arthur Boetes|
|Titel||A brief introduction to supersymmetry in quantum mechanics|
|Begeleiders||Jan de Boer, Jan Pieter van der Schaar|
|Faculteit||Faculteit der Natuurwetenschappen, Wiskunde en Informatica|
|Instituut/afd.||FNWI: Instituut voor Theoretische Fysica|
|Samenvatting||This thesis gives a basic introduction to supersymmetry in quantum|
Any supersymmetric system contains operators which obey the sl(1,1)
[Hs;Q] = [Hs;Qy] = 0;
fQ;Qyg ≡ QQy + QyQ = Hs;
fQ;Qg = fQy;Qyg = 0;
where Hs is the supersymmetric Hamiltonian. Q and Qy are operators
which carry the name supercharges. These supercharges leave the energy of a system invariant but exchange bosonic and fermionic degrees of freedom.
The symmetry in the name supersymmetry is due to the fact that the
supercharges commute with the Hamiltonian.
By supersymmetry one can see how two different potentials are linked
and share the same energy spectrum. To illustrate this property some
basic examples from "normal" quantum mechanics are treated, like the
infinite square well and the harmonic oscillator. The harmonic oscillator
example shows that despite the degeneracy the groundstate contains only a bosonic state. This is true for all unbroken supersymmetry systems.
However supersymmetry can also be broken, in this case the groundstate
has both a bosonic and a fermionic state. A tool to check whether or not supersymmetry is broken is the Witten index. This index is applicable in both quantum mechanics as well as quantum field theory. The breaking
of supersymmetry appears to be important, because it could explain why
supersymmetry has not been observed in nature. The supersymmetric Lagrangian
and the resulting equations of motion are calculated. This thesis
then moves on to superfields which contain anti commuting "coordinates".
These coordinates extend normal space-time and automatically manifest
supersymmetry. We move on to the Quantum Calogero Moser model using
supersymmetry. The Calogero Moser is a system containing N particles
which interact pairwise and can be subjected to three different kinds of potentials.
The thesis ends by giving examples from different fields in physics
like nuclear physics and the study black holes. Very important in the discovery and development of supersymmetry is particle physics. In this field every boson has a supersymmetric partner particle which is a fermion, and vice versa. It was introduced to solve the hierarchy problem of the Higgs mass. The absence of any data conforming unbroken supersymmetry implies that supersymmetry is either absent in nature or broken some time after the big bang. In any case the mathematics of supersymmetry are useful and elegant.
|Soort document|| scriptie bachelor|
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