The Widom-Sobolev formula for the free Dirac operator

With the proof of Widom’s conjecture giving new insights on the entanglement properties of the non-relativistic free Fermi gas, it is a natural question whether this situation extends to the relativistic case, where the single-particle Hamiltonian is given by the free Dirac operator.

In this talk I give a brief introduction to both the Widom-Sobolev formula as well as the free Dirac operator, and give an answer to the question above. I also talk about the strategy of the proof of this result, in particular I show how it can be reduced to an application of another result from my PhD thesis, a Widom-Sobolev formula for more general matrix-valued symbols.

The presented results were obtained in collaboration with Peter Müller.