dr Thomas Klaehn (ITF)

QCD gap equations and fractal structures? A simple model study

QCD's gap equations are self-consistent by their very nature. A typical method to solve them is to iterate an initial guess to a stable solution. As it is well known that more than one solution exists the question arises how and whether we obtain the correct one. We present a simple model where all solutions can be obtained from solving a polynomial equation and compare with results from the iterative method. We show that the method provides an in principle infinite amount of further solutions. To understand this behaviour as a consequence of the iterative approach we discuss fractal properties of the gap equation.