Marco Boers (Van Swinderen Institute, RUG)
Flow of quantum field theories as a dynamical system
Quantum field theory is the framework used to describe the fundamental constituents of matter, and their interactions. The strengths of these interactions are characterized by the ill-named ‘coupling constants’. They are not constants: The process of renormalization introduces a scale dependence in these couplings, which induces a flow in the space of theories. Of particular interest is the possible existence of fixed points of these flows, and the way they can emerge, merge, disappear, etc. (Homological) Conley index theory and bifurcation theory provide a great wealth of information on these processes, and can contribute to a better understanding of possible flows of quantum field theories, and related phenomena such as phase transitions.