# He who has read paper Phys Rev. on Dynamical Model of Elementary Particles

1. Feb 23, 2006

### Neitrino

He who has read paper Phys Rev. on "Dynamical Model of Elementary Particles"

My question concerns the bound (collective) states from paper “Dynamical model of Elementary particles”. So the bound (collective) states are considered in chapter IV.
I attach the file (extract from Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961) 345 – Dynamical Model of Elementary Particles Based on an Analogy with superconductivity) for your reference.

In this section in order to study the bound states & the coupling nature of these bound states with fermions they consider graphs in “ladder” approximation as shown in Fig No2 or 3b (Iteration of Graph shown in Fig 3a).

And to find the mass spectrum of bound states they find such values of q that this value makes J equal to 1 to make pole in expression 4.5. When writing expression for J(q) (graph with Gamma 5 vertexes) we obtain formula 4.6. Here I am confused – What is q?
Integration is over p variable… so as I know the loop Integral is taken over internal momentum, but here from denominator I was thinking that internal momentum is q
(since (p-1/2q) + (p+1/2q) “q”s will cancel each other). Also I am confused how to go from formula 4.6 to formula 4.6`).

So in this chapter different expressions of J(q) are evaluated for different vertexes.
In Pseudoscalar vertex cases the pole is J(0)=1. I think I say since the momentum q equals to zero in this pole so the pseudoscalar zero mass particle is manifested.
If I consider the q as a momentum of intermediate particle, then the graphs in Fig 3a and 4 can be considered equivalent, but if so it means that graph 3a transfers q momentum from point A to point B as I show in Fig4. And in this case I can no see the correspondence between 4.6 analytical expression and its graph in Fig 4

Thanks a lot

If I say something wrong pls advise me.

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