Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory

We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized directly in the SG field theory, we are rather concerned here with the corresponding N-soliton solutions. We present explicit expressions for their infinitesimal transformations and show that they are local in this case. Some preliminary stages about the quantization of the classical results presented in this paper are also given.