Jordan's boson representation for the one-dimensional two-fermion model

Marian Apostol

Jordan's theory of the boson representation of the fermion fields in one dimension is reviewed and generalised to the one-dimensional two-fermion model (TFM). It is shown that an additional constraint (Jordan's commutator) on the fermion fields has been overlooked so far by the theory of the TFM. This supplementary condition requires a particular cut-off procedure which has been little considered in recent times.

A. V. Kulikov

Marian Apostol, Victor Bârsan, Constantin Nantea

Jordan's boson representation and cut-off repolarization for the one-dimensional two-fermion model (TFT) is used to get the equivalence of the model with the two-dimensional Coulomb gas and sine-Gordon model. The scaling equations for the coupling constants are thereby obtained up to the third order.

Bent E. Sørensen

Bent Sørensen

C. Mantea, M Aposto, Victor Bârsan +3 more

The equivalence of the one-dimensional two-fermion model, on one hand, with the two-dimensional Coulomb gas and sine-Gordon models on the other is worked out by employing the Jordan boson representation and the point-splitting regularization. The distinction is made throughout between the bandwidth cut-off and momentum-transfer cut-off. It is shown that the coupling constants, both in the weak-coupling regime and near the Luther-Emery exact solution, scale with the momentum-transfer cut-off. The relationship between the bosonized form of the two-fermion model and the corresponding Fermi gas model is briefly discussed.