Pole structure and biharmonic fields in conformal QFT in four dimensions

Understand

Imposing Huygens' Principle in a 4D Wightman QFT puts strong constraints on its algebraic and analytic structure.

• These are best understood in terms of ``biharmonic fields'', whose properties reflect the presence of infinitely many conserved tensor currents.
• In particular, a universal third-order partial differential equation is derived for the most singular parts of connected scalar correlation functions.
• This PDE gives rise to novel restrictions on the pole structure of higher correlation functions.