Spectral gap problems in non-perturbative quantum theory

Non-perturbative problems of quantum theory with a lacking a small parameter are particularly challenging. Yet, several of the most important physical systems and models are exactly of this type. These include quantum Hall systems, O(N) sigma model, and the 4-dimensional Yang-Mills theory. These are enduring and very complex problems, but any progress achieved in this direction is of great value.


The efforts made by SwissMAP groups roughly fall into two categories:


  • spectral gap in the fractional quantum Hall effect
  • mass gap in spin systems with non-abelian symmetry