Supersymmetric quantum mechanics and path integrals
research submitted to the Faculty of Science, University of the Witwatersrand, in ful llment for the degree of Master of Science in Physics === Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained...
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| Format: | Others |
| Language: | en |
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2019
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| Online Access: | Ayad Mohamed Ali, Ahmed, (2019). Supersymmetric quantum mechanics and path itegrals, University of the Witwatersrand, https://hdl.handle.net/10539/28220 https://hdl.handle.net/10539/28220 |
| Summary: | research submitted to the Faculty of Science, University of the Witwatersrand,
in ful llment for the degree of Master of Science in Physics === Supersymmetry plays a main role in all current thinking about superstring theory. Indeed,
many remarkable properties of string theory have been explained using supersymmetry as
a tool. In this dissertation, we review the basics formulation of supersymmetric quantum
mechanics starting with introducing the concepts of supercharges and superalgebra. We
show that, if there is a supersymmetric state, it is the zero-energy ground state. If
such a state exists, the supersymmetry is unbroken otherwise it is broken. So far, there
has been no unbroken supersymmetry observed in nature, and if nature is described by
supersymmetry, it must be broken. In fact, supersymmetry may be broken spontaneously
at any order of perturbation theory, or dynamically due to non-perturbative e ects. The
goal of this dissertation is to study the methods of supersymmetry breaking. For this
purpose, a special attention is given to discuss the normalization of the ground state
of the supersymmetric harmonic oscillator. Then we explain that perturbation theory
gives us incorrect results for both the ground state wave function as well as the energy
spectrum and it fails to give an explanation to the supersymmetry breaking. Later in
the dissertation, a review of the uses of instantons in quantum mechanics is given. In
particular, instantons are used to compute the tunneling e ects within the path integral
approach to quantum mechanics. As a result, we give evidence that the instantons,
which are a non-perturbative e ect in quantum mechanics and can not be seen in
perturbation theory, leads to calculate the corrections to the ground state energy and
provides a possible explanation for the supersymmetry breaking. === E.K. 2019 |
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