Rigorous analysis of the Tomonaga model by means of Ward Identities and the renormalization group.

The Tomonaga model describes interacting 1d fermions with a linear dispersion relation and a bandwidth cutoff, which destroys local gauge invariance and makes the model not solvable. We rigorously obtain its Schwinger functions by combining Renormalization Group analysis with Ward Identities and a set of ``Correction Identities'', which relate the correction terms to formal Ward identities (due to cutoffs) with some Schwinger functions. Contrary to previous results, the use of the Luttinger model exact solution is completely avoided. Therefore this should be considered the first proof of what has been so far a conjecture: 1d interacting fermions can be constructed on the basis of a non perturbative analysis independent of the any exact solutions (of models which could be shown to have essentially the same beta function) and enterely based on a functional integral approach. The same method allows us the construction of essentially all 1d Luttinger liquid models.