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postgraduate thesis: Geometric quantization of fermions and complex bosons
Title | Geometric quantization of fermions and complex bosons |
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Authors | |
Advisors | Advisor(s):Wu, S |
Issue Date | 2013 |
Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
Citation | Hsu, S. [許紹輝]. (2013). Geometric quantization of fermions and complex bosons. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5043450 |
Abstract | Geometric quantization is a subject of finding irreducible representations of certain group or algebra and identifying those equivalent representations by geometric means. Geometric quantization of even dimensional fermionic system has been constructed based on the spinor representation of even dimensional Clifford algebras. Although geometric quantization of odd dimensional fermionic system has not been done, the existence of spinor representations in odd dimension indicates that the geometric quantization is possible.
In quantum field theory, charge conjungation can be defined on complex bosons and fermions. Without interaction, the particles and anti-particles essentially have same physical properties.
In this thesis, we will first recall the setup of geometric quantization of even dimensional fermion and bosons. Then we will show how to quantize odd dimensional fermion. After that, charge conjungation on complex fermion and boson will be defined and the remaining effort will be put on how to identify the Hilbert spaces produced by different charge conjungations. |
Degree | Master of Philosophy |
Subject | Geometry, Differential. Fermions - Mathematics. Bosons - Mathematics. |
Dept/Program | Mathematics |
Persistent Identifier | http://hdl.handle.net/10722/184263 |
HKU Library Item ID | b5043450 |
DC Field | Value | Language |
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dc.contributor.advisor | Wu, S | - |
dc.contributor.author | Hsu, Siu-fai. | - |
dc.contributor.author | 許紹輝. | - |
dc.date.accessioned | 2013-06-29T15:46:29Z | - |
dc.date.available | 2013-06-29T15:46:29Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | Hsu, S. [許紹輝]. (2013). Geometric quantization of fermions and complex bosons. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5043450 | - |
dc.identifier.uri | http://hdl.handle.net/10722/184263 | - |
dc.description.abstract | Geometric quantization is a subject of finding irreducible representations of certain group or algebra and identifying those equivalent representations by geometric means. Geometric quantization of even dimensional fermionic system has been constructed based on the spinor representation of even dimensional Clifford algebras. Although geometric quantization of odd dimensional fermionic system has not been done, the existence of spinor representations in odd dimension indicates that the geometric quantization is possible. In quantum field theory, charge conjungation can be defined on complex bosons and fermions. Without interaction, the particles and anti-particles essentially have same physical properties. In this thesis, we will first recall the setup of geometric quantization of even dimensional fermion and bosons. Then we will show how to quantize odd dimensional fermion. After that, charge conjungation on complex fermion and boson will be defined and the remaining effort will be put on how to identify the Hilbert spaces produced by different charge conjungations. | - |
dc.language | eng | - |
dc.publisher | The University of Hong Kong (Pokfulam, Hong Kong) | - |
dc.relation.ispartof | HKU Theses Online (HKUTO) | - |
dc.rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works. | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.source.uri | http://hub.hku.hk/bib/B50434500 | - |
dc.subject.lcsh | Geometry, Differential. | - |
dc.subject.lcsh | Fermions - Mathematics. | - |
dc.subject.lcsh | Bosons - Mathematics. | - |
dc.title | Geometric quantization of fermions and complex bosons | - |
dc.type | PG_Thesis | - |
dc.identifier.hkul | b5043450 | - |
dc.description.thesisname | Master of Philosophy | - |
dc.description.thesislevel | Master | - |
dc.description.thesisdiscipline | Mathematics | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.5353/th_b5043450 | - |
dc.date.hkucongregation | 2013 | - |
dc.identifier.mmsid | 991035342959703414 | - |