Localized Phase Space Representation of Dirac Particles: An Over-completeness Relation Approach
Lydia Taylor
A thorough understanding of the interplay between quantum and classical systems requires a solid grasp of what it means for a system to be quantum. Quantum phase space representations are an effective tool for achieving this goal, yet existing representations for quantum systems are typically non-local. A localized description is essential, particularly in the context of gravitational fields. Since gravitational field considerations are crucial for near-Earth quantum technologies, a localized phase space description could contribute to improving its performance and devise new strategies. In this work, we develop a framework for the phase space representation of Dirac particles, aiming to create a localized description of spin-1/2 particles. Using analytical techniques, we construct localized expressions that form the foundation for this phase space representation.
Matter-Wave Interferometry With Charged Particles: The Role of Vacuum Fluctuations
Nevan Keating
Quantum mechanics routinely describes events that seemingly defy conventional intuition. A particular example is a ”delayed-choice” measurement in a double slit experiment. This experiment involves ”tagging” a particle traveling through a double slit so that one can determine which-way information later on, seemingly forcing the particle to ”choose” a path before a measurement is made - in other words before a wavefunction collapses. However, one can show that the tagging itself is destroys the interference pattern, so that the measurement has no retrocausal effect. A recently proposed thought experiment suggests that by measuring the Coulomb field from a charged particle, one could instantaneously induce a wavefunction collapse. So, by measuring the Coulomb field from afar, one could collapse the wavefunction faster than light could travel between the particle and measuring device. At present, this paradox has only been resolved with the use of vacuum fluctuations, which limit the precision of measurements and prevent full collapse of the wavefunction. However, the Coulomb field in this paradox could be analogous to the tagging in a delayed-choice experiment. This thesis addresses the question whether the paradox could be seen as a delayed-choice experiment, offering an alternative solution to previous results
