Free theories are the simplest scale-invariant quantum field theories. In free theories, one makes a distinction between the elementary operators, which are the fields appearing in the Lagrangian, and the composite operators which are products of the elementary ones. The scaling dimension of an elementary operator O is determined by dimensional analysis from the Lagrangian (in four spacetime dimensions, it is 1 for elementary bosonic fields including the vector potentials, 3/2 for elementary fermionic fields etc.). This scaling dimension is called the classical dimension (the terms canonical dimension and engineering dimension are also used). A composite operator obtained by taking a product of two operators of dimensions Δ Δ 1 and Δ Δ 2 is a new operator whose dimension is the sum Δ Δ 1 + Δ Δ 2 .