content_image/314870.jpg content_image/314869.jpg content_image/314868.jpg content_image/314867.jpg content_image/314865.jpg content_image/314866.jpg
the most difficult step. 

Let us consider the bare connected n-point correlation function, Γ ( n ) B in φ 4 theory † . It is defined as 

<img src='content_image/314870.jpg'>

where φ$_{0}$ ( x ) refers to the bare fields, before renormalization. They are related to the renormalized fields by a rescaling: φ$_{0}$ ( x ) = Z 1 / 2 φ φ ( x ). The bare quantity, Γ ( n ) B is a function of the bare coupling constant, g$_{0}$ , and some cutoff, Λ. The renormalized quantity, Γ ( n ) R is a function of the renormalized coupling constant g and the renormalization scale M . 

<img src='content_image/314869.jpg'>

The bare theory is independent of the renormalization scale, M , so we can write 

It is easy to show that this equation can be rewritten as 

with the definitions 

<img src='content_image/314868.jpg'>

<img src='content_image/314867.jpg'>

<img src='content_image/314865.jpg'>

<img src='content_image/314866.jpg'>

