content_image/318467.jpg content_image/318468.jpg content_image/318469.jpg content_image/318470.jpg
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 

<img src='content_image/318467.jpg'>

<img src='content_image/318468.jpg'>

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 

<img src='content_image/318469.jpg'>

<img src='content_image/318470.jpg'>

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. 

## 1.2.7 Mass gap 

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 

