  The Future Circular Collider (FCC) is a crucial step forward to study new
Physics beyond the standard model and to test fundamental aspects as space-time
minimal length and Lorentz violations. As an example, a possible enhancement of
$e^+e^-$ pair production due to non-commutative effects, catalyzed by the huge
magnetic field produced at the beginning of a heavy ion collision at FCC, is
discussed. In noncommutative electrodynamics a free photon in the magnetic
background can produce a $e^+e^-$ pair. In particular for hard photons with
transverse energy $100-600$ GeV at the beginning of the collision and for a
particular kinematical setting of the pair , i.e. large total transverse
momentum in the reaction plane and invariant mass in the range $200-400$ MeV,
the non-commutative contribution, evaluated with the present bound of the
non-commuativity fundamental area , can be significant. Other, more exotic,
possible signatures of space-time non-commutativity are also considered.
