Phase structure of the Z(2) gauge and matter theory

We discuss the Z(2) theory using a hamiltonian formulation and emphasize the roles of gauge invariance and duality. Whereas the phases of the pure gauge theory can be characterized as electric-or magnetic-confining, one finds that in the presence of matter the two resulting phases can be characterized as matter-or gauge-screening. We investigate their properties by considering the exact vacua at the limiting points of the parameter space. Using such vacua in a mean-field approach we display the existence of a finite line of first-order phase transitions in the matter-screening phase and discuss its physical meaning.