Ward identity for non-relativistic fermions

Christoph Kopper, J. Magnen

V. I. Tokar

G. Morandi, Francesco Napoli

L. C. Costa, A. Ferraz, Vieri Mastropietro

Coupled fermionic chains are usually described by an effective model written in terms of bonding and anti-bonding fermionic fields with linear dispersion in the vicinities of the respective Fermi points. We derive for the first time exact Ward Identities (WI) for this model, proving the existence of chiral anomalies which verify the Adler-Bardeen non-renormalization property. Such WI are expected to play a crucial role in the understanding of the thermodynamic properties of the system. Our results are non-perturbative and are obtained analyzing Grassmann functional integrals by means of constructive quantum field theory methods.

Egon Marx

G. Benfatto, Vieri Mastropietro

The Tomonaga model describes interacting 1D fermions with a linear dispersion relation and a bandwidth cut-off, 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 cut-offs) with some Schwinger functions. Contrary to previous cases, 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 any exact solutions (of models which could be shown to have essentially the same beta function) and entirely based on a functional integral approach. The same method allows us to construct essentially all 1D Luttinger liquid models.