Elétrons fortemente correlacionados na vizinhança de uma transição de fase quântica

The aim of this work is to derive theWard Identity for the low energy effective theory of a fermionic system in the presence of a hyperbolic Fermi surface coupled with a U(1) gauge field in 2+1 dimensions. These identities are important because they establish requirements for the theory to be gauge invariant. We will see that the identity associated Ward Identity (WI) of the model is not preserved at 1-loop order. This feature signalizes the presence of a quantum anomaly. In other words, a classical symmetry is broken dynamically by quantum fluctuations. Furthermore, we are considering that the system is close to a Quantum Phase Transitions and in vicinity of a Quantum Critical Point the fermionic excitations near the Fermi surface, decay through a Landau damping mechanism. All this ingredients need to be take explicitly to account and this leads us to calculate the vertex corrections as well as self energies effects, which in this way lead to one particle propagators which have a non-trivial frequency dependence