There are many quantum field theories which, while not being exactly scale invariant, remain approximately scale invariant over a long range of distances. Such quantum field theories can be obtained by adding to free field theories interaction terms with small dimensionless couplings. For example, in four spacetime dimensions one can add quartic scalar couplings, Yukawa couplings, or gauge couplings. Scaling dimensions of operators in such theories can be expressed schematically as Δ Δ = Δ Δ 0 + γ γ ( g ) , where Δ Δ 0 is the dimension when all couplings are set to zero (i.e. the classical dimension), while γ γ ( g ) is called the anomalous dimension, and is expressed as a power series in the couplings collectively denoted as g . Such a separation of scaling dimensions into the classical and anomalous part is only meaningful when couplings are small, so that γ γ ( g ) is a small correction.