Supersymmetric quantum mechanics on n-dimensional manifolds
O'Connor, Michael
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https://hdl.handle.net/2142/22659
Description
Title
Supersymmetric quantum mechanics on n-dimensional manifolds
Author(s)
O'Connor, Michael
Issue Date
1990
Doctoral Committee Chair(s)
Stone, Michael
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Elementary Particles and High Energy
Language
eng
Abstract
In this thesis I investigate the properties of the supersymmetric path integral on Riemannian manifolds. Chapter 1 is a brief introduction to supersymmetric quantum mechanics. In Chapter 2 I show that the supersymmetric path integral can be defined as the continuum limit of a discrete supersymmetric path integral. In Chapter 3 I show that point canonical transformations in the path integral for ordinary quantum mechanics can be performed naively provided one uses the supersymmetric path integral. Chapter 4 generalizes the results of chapter 3 to include the propagation of all the fermion sectors in supersymmetric quantum mechanics. In Chapter 5 I show how the properties of supersymmetric quantum mechanics can be used to investigate topological quantum mechanics.
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