Quantum phenomena and shape dynamics - Dündar, Furkan Semih. (Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018)
In this thesis, we considered quantum phenomena (Unruh eﬀect) in Shape Dy namics, version of Bohmian Mechanics that is compatible with Mach’s Principle, and a solution (gravitational collapse of a spherically symmetric thin shell of dust) of Shape Dynamics. First, it is interesting that we proved the existence of Unruh radiation in Shape Dynamics where there is no Lorentz symmetry and no unbounded ﬂat space. In order to detect the existence of Unruh eﬀect we used an Unruh-DeWitt detector. Second, a toy model for Shape Dynamics that is suitable for particle interactions is considered. It brings three constraints for solutions: Energy constraint, angular mo mentum constraint and dilational momentum constraint. We applied these constraints to particle variables of Bohmian Mechanics and obtained a constrained Bohmian Me chanics that is Machian. Third, we considered a spherically symmetric thins shell of dust in Shape Dynamics in a space manifold which is [0,1]×S2. We calculated the symplectic form and its inverse. The phase space variables turned out to be the coordinate radius and total momentum of the shell, the expectation value of the trace of the metric momentum, and the volume of the space. We laid the foundations for future research.
Keywords: Shape theory (Topology); Quantum theory.