Perturbation theory in the radial quantization approach and the expectation values of exponential fields in the sine-Gordon model

We have developed a perturbation theory, based on the radial quantization ot the massive Thirring model (MTM). It is remarkable that the apparent difficulty in radial quantization of massive theories, namely, the explicit 'time' dependence of the Hamiltonian, may be successfully overcome. In this framework, in first order of the coupling constant of MTM, we calculate the vacuum-vacuum amplitude with arbitrary twisted boundary conditions imposed on the Fermi fields. In terms of sine-Gordon theory these amplitudes are nothing other than the expectation values of exponential fields 〈exp iaφ(0)〉. The result we have obtained coincides with the analogous calculations recently carried out in a dual, angular quantization approach by one of the authors and completely agrees with the exact formula conjectured by Lukyanov and Zamolodchikov.