A First Taste of Quantum Gravity Effects: Deforming Phase Spaces with the Heisenberg Double
| dc.contributor.author | Maitland, Anson | |
| dc.date.accessioned | 2014-09-25T17:49:13Z | |
| dc.date.available | 2014-09-25T17:49:13Z | |
| dc.date.issued | 2014-09-25 | |
| dc.date.submitted | 2014 | |
| dc.description.abstract | We present a well-defined framework to deform the phase spaces of classical particles. These new phase spaces, called Heisenberg doubles, provide a laboratory to probe the effects of quantum gravity. In particular, they allow us to equip momentum space with a non-abelian group structure by the introduction of a single deformation parameter. In order to connect Heisenberg doubles with classical phase spaces we begin with a review of Hamiltonian systems, symmetries and conservation laws in the classical framework. Next, we provide a comprehensive review of the theory behind Poisson-Lie groups, including Lie bialgebras and the construction of the Drinfeld double. Lastly, we build the Heisenberg double from Poisson-Lie group components. We then identify the Heisenberg double as a deformation of the cotangent bundle of Lie groups and extend many of the notions of classical Hamiltonian systems to this new picture with Poisson-Lie symmetries. As an example, we look at a new presentation of the deformed rotator. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/8866 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | quantum gravity | en |
| dc.subject | phase space | en |
| dc.subject | Heisenberg double | en |
| dc.subject | Poisson-Lie group | en |
| dc.subject.program | Applied Mathematics | en |
| dc.title | A First Taste of Quantum Gravity Effects: Deforming Phase Spaces with the Heisenberg Double | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Applied Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |