p − 2(1 − γ ( g ∗ $^{))}$. The complex interactions of the quantum field theory have af- fected the law of rescaling. Finally, since the fixed point is reached at large p , it is known as an ultraviolet fixed point. An analysis of graph 1.3(b) follows similar lines. Near the fixed point the β function can be approximated by which has the solution This means that for sufficiently small p , the integral in the exponential of (1.8) will be dominated by those values of p where g ( p ) is close to $^{g}$∗ , giving Because this occurs at small p , this fixed point is called an infrared fixed point. Once again, the complex interactions of the field theory have affected the law of rescaling. For this reason, the γ ( g ) function is commonly known as the anomalous dimension , even if there is no fixed point in the theory. Another feature of QCD, and yet to be proved rigorously by anybody, is that of a mass gap. A quantum field theory is said to have a mass gap if the energy spectrum has a positive greatest lower bound, but does not 17 1.2.7 Mass gap β ∼ + B ( g − $^{g}$∗ ) (1.27) ¯ g ( p ) = $^{g}$∗ + C ( p M ) B (1.28) G ( p ) ≈ G ( $^{g}$∗ ) exp [ − (log p M 2(1 − γ ( $^{g}$∗ )) ] (1.29) 1 γ ( g ∗ ) ≈ C ( 1 p 2 ) 1 − γ ( g ∗ ) (1.30)