Locality from dynamics

Project level: Honours

All fundamental interactions known in nature are local: only close-by systems can interact. But where does the very notion of closeness come from? Ultimately, we only learn about spatial relations through physical systems, it should thus be possible to understand the locality of interactions without pre-assuming the existence of an absolute space.

The aim of the project is to derive the local structure of quantum systems from properties of dynamics alone, with no reference to any underlying geometry. Formally, the task is to derive a decomposition of Hilbert space in tensor factors, with each factor representing a local subsystem, from basis-independent properties of the Hamiltonian.