Linearity in the renormalisation group equations
Seminars
Bogoliubov Laboratory of Theoretical Physics
Seminar on Quantum Field Theory
Date and Time: Tuesday, 25 November 2025, at 11:00 AM
Venue: Blokhintsev Lecture Hall, Bogoliubov Laboratory of Theoretical Physics, online on Zoom
Information about the seminar and link to join
Seminar topic: “Linearity in the renormalisation group equations”
Speaker: Denis Tolkachev (BLTP JINR; Stepanov Institute of Physics of the National Academy of Sciences of Belarus)
The speaker will demonstrate an approach to obtaining universal equations that allow summing an infinite series of singular and logarithmic contributions in an arbitrary local quantum field theory in an arbitrary order of perturbation theory. Next, this approach will be demonstrated using the example of an arbitrary scalar effective potential, and a set of graphical rules for writing general equations in arbitrary order of perturbation theory for this model will be described. The resulting equations, except for the equation for the leading contributions, turn out to be linear. Since these equations are absolutely general, they contain, to their limit, the perturbative behaviour of a distinguished class of models called renormalisable. However, it is well known that the equation for the running coupling in the renormalised theory is nonlinear. The resolution of this contradiction leads to interesting, previously unknown solutions in a renormalisable model.