The Basic Models of Quantum Field Theory

Let us consider the four-dimensional Minkowski space-time with the coordinates x^μ;μ = 0,1,2,3 and the metric η_μυ = diag(l, – 1, – 1, – 1). A real or complex function, which is defined on Minkowski space-time is called a field. Usually it is accepted that the fields are the geometrical objects, i.e. are the tensors of some rank or spinors relative to the Lorentz transformations. In quantum field theory it is postulated that the fields are the fundamental physical concepts in terms of which the interactions of the elementary particles are described.