A How to relate the expansion term to Feynman diagrams

[chern]

I learn quantum field theory using the book of " quantum field theory in a nutshell" by A. Zee. But I am confuse when I read the content about the "baby problem" at the beginning of "1.7 Feynman Diagrams". In that section, author get the term of order λ and [J][/4] by -(λ/4!)[(d/dJ)][/4] [1/4![2[m][/2]][/4]][J][/8]. My question is how to draw the figures in I.7.1 according to the result? why are there three figures? There is only one term, why do we get three figures? Thank you !

 

[azntoon]

The three figures in I.7.1 represent the different ways in which the term λ/4![(d/dJ)][/4] [1/4![2[m][/2]][/4]][J][/8] can be represented as a Feynman diagram. The first figure shows the initial starting point of the diagram: the term λ/4!. The second figure shows the diagram after the action of the derivative (d/dJ). The third figure shows the diagram after the action of the factors 1/4![2[m][/2]][/4] and J/8. Each of these diagrams represents the same mathematical expression, but they may help to visualize it in different ways. For example, the third figure might make it easier to identify the number of factors in the expression, while the second figure might make it easier to understand how the derivative (d/dJ) acted on the expression.