Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem

摘要

The authors show that renormalization in quantum field theory is a special211u001einstance of a general mathematical procedure of multiplicative extraction of 211u001efinite values based on the Riemann-Hilbert problem. The authors show that, using 211u001edimensional regularization, the bare data in quantum field theory delivers a loop 211u001e(where z is now the deviation from 4 of the complex dimension) of elements of the 211u001edecorated Butcher group (obtained using the Milnor-Moore theorem from the Kreimer 211u001eHopf algebra of renormalization) and that the above general procedure delivers 211u001ethe renormalized physical theory in the minimal substraction scheme.