Seminar: Infrared divergences and the choice of renormalisation scheme

Quantum Field Theoretical calculations are known to contain infinities at intermediate steps, stemming from assumptions that spacetime is continuous down to arbitrarily small distances (ultraviolet divergences) or that interactions do not fall off fast enough with distance (infrared divergences). These two regimes do not interact physically. They can, however, become intertwined by the regularisation/renormalisation procedure used to obtain meaningful expressions at intermediate steps, especially in the context of dimensional regularisation.

In this talk, I will discuss some theoretical issues arising in the calculation of next-to-leading-order corrections to processes renormalised in non-on-shell schemes. I will explain the origin of infrared and ultraviolet divergences. I will illustrate with a simple example why the mass assignment requested by the Lehmann–Symanzik–Zimmermann reduction formula yields an off-shell regularisation that gives the wrong result if applied naively. Finally, I will provide a prescription for obtaining correct results, based on unitarity and Cutkosky's cutting rules.