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

Abstract

We have developed a perturbation theory, based on the radial quantization of 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 ia(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.