Form function of an isolated chain exact results

2 Form function of an isolated chain exact results 

The form function H(q) associated with the continuous model is a function /i(x, z) [see (13.1.152)] and this function can be expanded in powers of z 

In principle, h(x) can be calculated directly by starting from (13.1.148) and (13.1.153). It is also possible to get the result through field theory. 

Using renormalization theory, Witten and Schafer2 calculated the expansion of the form factor, in the limit z - cc, to first order in e = 4 — d and to second-order in x. Using the notation introduced above, we can express their result as follows 

On the other hand, it is not difficult to calculate hrx to first-order in e, by starting from eqn (13.1.153). In this way, one obtains (des Cloizeaux and Duplantier)27 for x 1 

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