Lorentzian fermionic action by twisting Euclidean spectral triples

We show how the twisting of spectral triples induces a transition from Euclidean to Lorentzian noncommutative geometry at level fermionic action. More specifically, we compute action for closed manifold, then that two-sheet and finally triple electrodynamics in signature. obtain Weyl Dirac equations signature (and temporal gauge). The twisted is shown be invariant under an Lorentz group. This permits us interpret field 1-form parametrises fluctuation manifold as (dual) energy-momentum 4-vector.