ABSTRACT
This chapter reviews the construction of the exact solution of the model from the functional integral point of view. Quantum field theory is a structure at the root of our understanding of physical world from the subnuclear scales to the astrophysical and the cosmological ones. The concept of a quantum field is very rich and poorly understood although much progress has been achieved over some 70 years of its history. Due to the infinite-dimensional nature of the conformal symmetry in two space-time dimensions, the two-dimensional models of conformal field theory lend themselves to a genuinely non-perturbative approach based on the infinite symmetries and the concept of the operator product expansion. Non-linear sigma models describe field theories with fields taking values in manifolds. The formalism of Green functions encoding the action of field operators constitutes a traditional tool in quantum field theory.
