  We study a complex free scalar field theory on a noncommutative background
spacetime called $\kappa$-Minkowski. In particular we address the problem of
second quantization. We obtain the algebra of creation and annihilation
operators in an explicitly covariant way. Our procedure does not use
canonical/Hamiltonian formulations, which turn out to be ill-defined in our
context. Instead we work in a spacetime covariant way by introducing a
noncommutative Pauli-Jordan function. This function is obtained as a
generalization of the ordinary, commutative, one by taking into account the
constraints imposed by the symmetries of our noncommutative spacetime. The
Pauli-Jordan function is later employed to study the structure of the light
cone in $\kappa$-Minkowski spacetime, and to draw conclusions on the
superluminal propagation of signals.
