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The generalisation of equation (5.8) is 

Using the fact v ( q, r ′ ) = [ K$_{1}$ ( r ) ∂$_{r}$G ( q ; r, r ′ $^{)]$_{r}$$_{=}$}$∞, we find 

Comparing this to (6.11) we identify the rho decay constant as: 

## 6.2.2 Axial sector 

<img src='content_image/304725.jpg'>

<img src='content_image/304726.jpg'>

<img src='content_image/304727.jpg'>

The axial vector field is defined as A a µ = ( A a Lµ − A a $_{Rµ}$). We choose the gauge such that A$_{ar}$ ( x, r ) = 0 and A µ a = A µ a ⊥ + ∂ $^{µ}$φ . There are three equations of motion: one for each of the a$_{1}$ meson field, the π field and the longitudinal axial gauge field φ : 

<img src='content_image/304728.jpg'>

<img src='content_image/304729.jpg'>

<img src='content_image/304730.jpg'>

where K$_{3}$ ( r ) = Hf 3 / 2 − δ/ 2+Δ / $^{2}$h$^{3}$r$^{3}$(1 + ˙ σ $^{2}$) − 1 / 2 and K$_{4}$ ( r ) = f 1+Δ / $^{2}$h$^{2}$r$^{3}$(1 + ˙ σ $^{2}$) − 1 / $^{2}$, and we have separated $^{A}$⊥ as $^{A$_{i}$}$⊥ ( x, r ) = A ( q, r ) exp( iqx ). 

Looking for the normalizable solutions to (6.16) requires us to set the boundary conditions ψ$_{a}$$_{1}$ ( ∞ ) = 0 and ∂$_{r}$ψ$_{a}$$_{1}$ (0) = 0. We can then predict the a$_{1}$ meson mass spectrum. And in an almost identical analysis to that 

