Gauge-invariant resummation formalism and unitarity in non-commutative QED

We re-examine the perturbative properties of four-dimensional non-com\-mutative QED by extending the pinch techniques to the θ-deformed case. The explicit independence of the pinched gluon self-energy from gauge-fixing parameters and the absence of unphysical thresholds in the resummed propagators permits a complete check of the optical theorem for the off-shell two-point function. The known tachyonic dispersion relations are recovered within this framework, as well as their improved version in the (softly-broken) SUSY case. These applications should be considered as a first step in constructing gauge-invariant truncations of the Schwinger-Dyson equations in the non-commutative case. An interesting result of our formalism appears when considering the theory in two dimensions: we observe a finite gauge-invariant contribution to the photon mass because of a novel incarnation of IR/UV mixing, which survives the commutative limit when matter is present. © SISSA 2006