Significance of Order in Feynman Diagrams

[Demon117]

I've been doing some review of particle physics in Griffiths and I came across this statement that really didn't stand out to me before.

"the idea is to draw all the diagrams contributing to the process in question (up to a desired order), calculate the amplitude (M) for each one, and add them up to get the total amplitude"

I would like to know what is the significance of the "up to a desired order" statement? I've read in books about quantum field theory that the idea is we are actually using a perturbation procedure in the Feynman diagram formalism. Is there any evidence to that claim or am I confusing it with something else?

Or instead is the order of a process just have to do with the number of external/internal lines in a diagram?

 

[kevinferreira]

Have you seen Dyson series? That helps... Assuming a weak interaction, associated with a weak coupling constant (as the electric charge in QEd), we obtain by a perturbative treatment of the theory a solution in terms of an increasing exponent of the coupling constant, which have less and less relevance as we assume the constant is weak.

Feynman diagrams, together with its Feynman rules, are an easy and quick way of resuming a fastidious mathematical procedure. Feynman diagrams in different theories have orders, corresponding to the orders of the perturbative treatment in the 'fastidious mathematical procedure'. If the whole math thing seems absurd when compared to the power of Feynman diagrams, I think it is needed to understand deeply the Feynman procedure. Try at least to look up for Feynman rules, which give some insight on the 'order' of a Feynman diagram.

 

[andrien]

for a given process there are infinity of feynman diagrams.The order is decided by the number of vertex it contains.To a desired accuracy you will have to go to a desired order.