A question about T-matrix in two-body scattering

[Bin Jiang]

TL;DR

How to understand T-matrix in two-body scattering? Especially how to understand "leading order" in the text.

How can we understand T-matrix in two-body scattering? Especially term "leading order" in the text. In addition, how to understand the connection between fig2.3 and equation 2.24-2.26?
Thanks.

 

[DrDu]

Summary:: How to understand T-matrix in two-body scattering? Especially how to understand "leading order" in the text.

How can we understand T-matrix in two-body scattering? Especially term "leading order" in the text. In addition, how to understand the connection between fig2.3 and equation 2.24-2.26?
Thanks.

The T-matrix, whose precise definition must be given somewhere else in the book, can be expanded into a power series in the coupling strength g. The zeroth- order term is trivial, as it corresponds to no scattering at all. The term containing the lowest non-vanishing power of g (g^1 in this example) is the leading order.
The diagrams in fig. 2.3 are so called Feynman-diagrams and there are rules how they are in a one to one correspondence with actual terms in the perturbation series.