We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "maximal analyticity" and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the "off-shell" Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the Sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. In particular we calculate the three particle form factor of the soliton field, carry out a consistency check against the Thirring model perturbation theory and thus confirm the general formalism.
Karowski Replies: Huse' found by Monte Carlo simulations that the Euler characteristic of a self-avoiding random surface model ^ is negative at the critical point. I think this result is correct. This point was not one of the main topics of our Letter, but rather phase diagrams of some self-avoiding random surface models in three and four dimensions. Simulating our random surfaces we observed that the "mean curvature" vanished at the critical temperature (within error bars). Thus we speculated as a by-product that "this flatness might be related to scale invariance."Unfortunately, in writing our Letter we changed the notation, whereby there appeared some errors: The quantity in Eq. (8) and Figs. 1 and 2 is not the "Euler characteristic" X ^ sites ^ links ' ^ plaquettes > but twice the diff*erence of components and handles:V/ = 2(rtcomp"~Whand) •In our paper the self-avoiding surfaces should approximate bubbles of microemulsions. Therefore the quantity \lf and not x represents the mean curvature. This is because, e.g., two cubes touching at one vertex are con-sidered to be distinct. Hence there is no negative contribution to the curvature as the quantity x would suggest. Moreover, the appearance of a "droplet phase" in the phase diagrams of Fig. 4 compared to Fig. 3 shows that the quantity \if (not x^ plays a more interesting role for our self-avoiding random surfaces. Incited by Huse's Comment, I investigated the "flatness" property near the critical point more carefully. Using my old program I found <;t:)=0 at j3 =0.364 and {\ff)-Q at ^=0.356, whereas the critical point is at /?=0.353.
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