Coleman correspondence and non-stationary Ruijsenaars function

Quantum field theory (QFT) is an important tool in theoretical physics, with many successful applications in different areas of physics.

It has also inspired the development of new mathematics like the Atiyah-Singer index theorem, affine Kac-Moody algebras or the Schramm-Loewner evolution, and this has in turn provided new powerful tools for phycistists.Conformal field theory (CFT) is one class of QFT models where an excellent mathematical understanding has been reached in recent years.

This project aims at reaching a thorough mathematical understanding of a QFT known as massive Thirring model (mTM), which is an outstanding example of an integrable massive QFT beyond CFT.

I propose to use recent results in the mathematical theory of special functions or, to be more specific, Macdonald-Ruijsenaars theory, to construct the massive Thirring model (mTM), and to make precise and prove the Coleman correspondence that the mTM is equivalent to quantum sine-Gordon theory.

The idea is to enlarge a known q-deformation of CFT developed in Macdonald theory to a proper QFT with local massive fields and, through that, use Macdonald theory to construct and solve the mTM.

I hope that this will also lead us to the solution of an outstanding problem in the theory of quantum Calogero-Moser-Ruijsenaars systems: to find the mother system of all known A-type Calogero-Moser-Ruijsenaars models having Shiraishi´s non-stationary Ruijsenaars function as exact  eigenfunction.