In quantum field theory a state is strictly localized to a region X in spacetime if the expectation value of any local observable outside X is equal to that in vacuum. Strictly localized states are important and interesting from a fundamental point of view. In addition, it is interesting to characterize these states from a practical point of view, since they correspond to states produced by on-demand sources.
There are many interesting questions to consider (see below). It is not realistic to answer all questions. It is possible that two students collaborate and divide tasks between them. The work will involve mathematical analysis, possibly with some analytical computer tools and/or numerics. A PhD student and the supervisor will be involved.
Specific tasks for the project
- How well can a strictly localized state approximate a single-boson or single-fermion state, or any other desired state?
- Determine the detailed properties of strictly localized states, e.g. similarly to the well-known properties of coherent states.
- How can we explicitly generate any desired state locally (as described in the Reeh-Schlieder theorem)?