ABSTRACT
This chapter describes the simplest method—the strong coupling expansion. It explains the strong coupling expansion in the Ising model. After the phase transition point a condensate of the particles is formed and the strong coupling expansion is impossible. It is an interesting exercise to establish the correspondence between Shrodinger perturbation theory for the Hamiltonian and diagrams for the Euclidean approach. The chapter describes that in the strong coupling region all systems with global symmetries look roughly the same. In all cases we had massive point like excitations which propagate through the lattice. In the Non-Abelian cases with D=2 this picture remained valid even for small coupling. In the case of a gauge system the strong coupling region is again rather insensitive to the type of symmetry. However, gauge invariance introduces qualitatively new features to this region which will be discussed.
