In this thesis we focus on two elementary unstable quantum systems, the inverted
harmonic oscillator and the inverse square potential, using the methods of effective
field theory (EFT) and the renormalization group (RG). We demonstrate that the
phenomenon of fall to the centre associated with the inverse square potential is an
example of a PT symmetry breaking transition. We also demonstrate a mapping
between the inverted harmonic oscillator and the inverse square potential including a
one-to-one mapping between the quantum states and boundary conditions using an
EFT framework in a renormalization group invariant way. We apply these methods
to the phenomenon of Schwinger pair production and study finite size effects using
the RG scheme for the quantum inverted harmonic oscillator. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/30238 |
| Date | January 2024 |
| Creators | Sundaram, Sriram |
| Contributors | O'Dell, Duncan, Physics and Astronomy |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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