ABSTRACT
This chapter discusses a specific mechanism for gap generation, which is especially important in Abelian systems and will also play some role in nonabelian ones. The only interest of Ising model for research workers is that it provides the simplest demonstration of a phenomenon present in more complicated systems. The point research workers intend to examine is that this model in any finite order of perturbation theory has apparently broken symmetry, whereas in reality the symmetry is restored. At the same time research workers know from quantum mechanics that the ground state of this theory is described by an even ψ-function and therefore is nondegenerate, with restored symmetry. The chapter examines the case of Abelian gauge theories. The nontriviality comes from the fact that the vector potential has certain angular properties which force research workers to account for the analogues of vortices or dislocations in the functional integral.
