Reciprocal space expansions for an isolated chain

Diagrams can also correspond to Fourier transforms, and such a representation is often convenient. We can use it either to calculate +3T(s) or to calculate the Fourier transform of a restricted partition function + J (r,. . . , rE sly. sE,S), defined by 

When the volume is infinite, this relation takes the form 

To determine the diagrammatic representation of 2 (S) or of (k . . ., kE yu.. . , 3 E S) in reciprocal space, we must introduce the Fourier transform of the interaction terms 

In the same way, we must express the factors associated with the polymer segments in the form of Fourier transforms. Thus, the factor associated with a segment of area Sj, joining two successive interaction points with position vectors r, and r, has the form 

This formula can be interpreted by saying that the vector q is transferred from interaction point j-l to interaction point j (or - q from interaction point j to interaction point j) and eqn (10.4.22) can be interpreted in the same manner. 

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