Average action for fermions and spontaneous symmetry breaking in the standard model

The average action is a new tool for investigating spontaneous symmetry breaking in elementary particle theory. It extends the scope of standard perturbation theory and the standard effective potential. The aim of this work is a full treatment of the average potential for a coupled system of scalars and fermions. It leads to evolution equations that describe how couplings and masses change with the length scale k-1 where the theory is defined. One finds that fermions and scalars contribute with opposite sign to the dependence of the scalar mass term m2 on the scale k-1. We discuss the possibility that a 'balance effect' between these contributions leads to an infrared stable fixpoint in the evolution of the ratio m2(k)/k2. Such a behavior would result in self-organizing criticality and could naturally explain a small gauge hierarchy. Furthermore we study the inner region of the average potential (for small scalar fields) where standard perturbation theory breaks down. The minimum which occurs in the spontaneously broken phase in the outer region of the average potential is established to be a global minimum of the theory and thus determines the vacuum expectation value of the scalar field. (orig.)