Seminar "Localizability in bandlimited and ordinary quantum field theory" by Jason Pye
Date: Tuesday, January 28th
Speaker: Jason Pye, Ph.D. Student, University of Waterloo
Title: Localizability in bandlimited and ordinary quantum field theory
It has long been argued that combining the uncertainty principle with gravity will lead to an effective minimum length at the Planck scale. In the first part of this talk, I will discuss a model for quantum field theory possessing a minimum length scale which respects continuous Euclidean or even Lorentzian spacetime symmetries. The Euclidean case consists of the application of the Shannon sampling theorem of classical information theory, which establishes the equivalence between continuous and discrete representations of information. Quantum fields in this model exhibit a finite density of information and a corresponding regularization of the entanglement of the vacuum, as I will demonstrate in detail. I will then examine the Lorentzian symmetry generalization, which leads to a Lorentz-invariant analogue of bandlimitation, and I will discuss the nature of the corresponding sampling theory.
In the second part of the talk, I will be discussing obstructions to the consistent description of an ordinary relativistic quantum field theory as a theory of localizable particles. Specifically, I will trace exactly how such obstructions arise in the regime between nonrelativistic quantum mechanics and relativistic quantum field theory. Perhaps unexpectedly, in the nonrelativistic limit of QFT there are persisting issues with the localizability of particle states. Related via the Reeh-Schlieder theorem, I also show that the fate of ground state entanglement is nontrivial in this limit.