List of Titles

Authors: Sixaba, Vuyile
Date: 2018
Subjects: Special relativity (Physics) , Quantum gravity , Quantum theory , Geometry , Heisenberg uncertainty principle
Language: English
Type: text , Thesis , Masters , MSc
Identifier: http://hdl.handle.net/10962/59478 , vital:27615
Description: We undertake a study of the classical regime in which Planck's constant and Newton's gravitational constant are negligible, but not their ratio, the Planck mass, in hopes that this could possibly lead to testable quantum gravity (QG) effects in a classical regime. In this quest for QG phenomenology we consider modifications of the standard dispersion relation of a free particle known as deformed special relativity (DSR). We try to geometrize DSR to find the geometric origin of the spacetime and momentum space. In particular, we adopt the framework of Hamilton geometry which is set up on phase space, as the cotangent bundle of configuration space in order to derive a purely phase space formulation of DSR. This is necessary when one wants to understand potential links of DSR with modifications of quantum mechanics such as Generalised Uncertainty Principles. It is subsequently observed that space-time and momentum space emerge naturally as curved and intertwined spaces. In conclusion we mention examples and applications of this framework as well as potential future developments.
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Date Issued: 2018

Authors: Henninger, Helen Clare
Date: 2012
Subjects: Geometry , Symmetry groups , Symmetry (Mathematics)
Language: English
Type: Thesis , Masters , MSc
Identifier: vital:5432 , http://hdl.handle.net/10962/d1018232
Description: In this thesis we study left-invariant control offine systems on the symmetry group of a. model of hyperbolic plane geometry, the matrix Lie group SO(1, 2)₀. We determine that there are 10 distinct classes of such control systems and for typical elements of two of these classes we provide solutions of the left-invariant optimal wntrol problem with quauratic costs. Under the identification of the Lie allgebra .so(l, 2) with Minkowski spacetime R¹̕'², we construct a controllabilility criterion for all left-invariant control affine systems on 50(1. 2)₀ which in the inhomogeneous case depends only on the presence or absence of an element in the image of the system's trace in R¹̕ ²which is identifiable using the inner product. For the solutions of both the optimal control problems, we provide explicit expressions in terms of Jacobi elliptic functions for the solutions of the reduced extremal equations and determine the nonlinear stability of the equilibrium points.
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Date Issued: 2012

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