A variety of quantum systems exhibit Weyl points in th eir spectra, where two bands cross in a point of three dimensional parameter spacewith a conical dispersion in the vicinity of the point. In this talk, the soft constraint regime is considered theoretically, where the parameters are dynamical quantum variables. It is shown that in general the soft constraint in semi-classical limit results in Weyl discs, where two states are (almost) degenerate in a finite two-dimensional region of the thee dimensional space. Concrete calculations are provided for two setups: Weyl points in four-terminal superconducting structures and a Weyl exciton that is a bound state of a Weyl electron and a massive hole.

Work with Janis Erdmanis and Yuli V. Nazarov.