Nadine Stritzelberger | Applied Math, University of Waterloo
Explorations in Quantum Theory, General Relativity and Cosmology
In this seminar I will discuss my research, which is concerned with three different topics in the related fields of Quantum Theory, General Relativity and Cosmology.
Delocalization excitation and radiation: In this project we conjecture a new mechanism by which particles can be produced. We investigate a localized small quantum system, such as an atom or ion, moving through a quantum field in the vacuum state. When left alone, the initially localized quantum system delocalizes and its centre of mass wavefunction spreads. We predict that the therefore time-dependent coupling of the delocalizing system to a quantum field leads to a nonzero probability for the system to get excited while emitting a field quantum. I will discuss these newly-predicted processes, which we refer to as delocalization excitation and delocalization radiation respectively.
Lorentzian inverse spectral geometry: The discipline of inverse spectral geometry is concerned with the extent to which a metric on a manifold can be reconstructed from the spectra of differential operators. Establishing inverse spectral geometry for Lorentzian manifolds in four dimensions would enable a reformulation of general relativity---with the diffeomorphism-invariant spectra of differential operators as gravitational degrees of freedom---suited for straightforward quantization. I will discuss our attempts to reconstruct the geometric degrees of freedom of Lorentzian and Riemannian manifolds in two dimensions from the spectrum of the d'Alembert operator using Lagrange inversion. We aim at extending our results to four dimensional, conformally flat, Lorentzian manifolds such as to reformulate cosmological gravitational dynamics in terms of the eigenvalues of differential operators and study quantum cosmology within this framework.
Gravitational lensing in birefringent spacetimes: For any given predictive and quantizable matter dynamics, the underlying gravitational dynamics for the geometric background already follow as a solution to a countably infinite set of linear homogeneous partial differential equations, derived solely from the matter dynamics. This previously obtained result has important implications in the context of constructing consistent modified gravitational theories. In this project we consider the weak field gravitational dynamics of the tensorial geometry which underlies the most general linear theory of electrodynamics. This matter theory is of particular interest in the context of standard model extensions, as it reduces to Maxwell electrodynamics in a limit case, while in its general form allowing to describe phenomena such as birefringence in vacuo. We explore the--possibly experimentally testable--imprints which the existence of vacuum birefringence in nature would leave on weak gravitational lensing.