content_image/299366.jpg content_image/299365.jpg content_image/299364.jpg content_image/299363.jpg content_image/299362.jpg
and consequently $^{[}$d $^{d}$x ] = − d . By a similar argument it can be shown that 

<img src='content_image/299366.jpg'>

This can be used to determine the dimensions of the fields and parameters appearing in the QCD Lagrangian (1.40). For instance, from the quark term we can show that 

<img src='content_image/299365.jpg'>

because the Dirac Gamma matrix is dimensionless. From the gluon term we find that 

<img src='content_image/299364.jpg'>

The units of the coupling can be determined from the quark-gluon interaction term: 

<img src='content_image/299363.jpg'>

because the Gell-Mann matrix is dimensionless. The renormalization scale has [ µ ] = 1, therefore 

and hence α is an appropriate expansion parameter in d -dimensions. 

<img src='content_image/299362.jpg'>

