content_image/300198.jpg content_image/300207.jpg content_image/300208.jpg
tons [26–28]. 

<img src='content_image/300198.jpg'>

If we represent the vector current two-point function as figure 1.4, then one contribution to the vector two-point current will be that of figure 1.5. 

It can be shown [29, 30] that at large N, the mesons form an infinite, stable spectrum and that the vector two-point current is given by the sum over all meson and glueball resonances (with the correct quantum numbers), such as that in figure 1.5: 

<img src='content_image/300207.jpg'>

The axial vector current two-point function at large N, Π$_{P}$ ( − q $^{2}$), is almost identical: 

## Axial Current Anomaly 

<img src='content_image/300208.jpg'>

(1.31) also possesses a U (1)$_{L}$ ⊗ U (1)$_{R}$ symmetry which we have yet to men- tion. Whereas the SU (2) symmetries mixed the up and down quarks, the U (1) symmetries act to add a phase to the entire spinor. Classically, we have 

