  The most popular noncommutative field theories are characterized by a matrix
parameter theta^(mu,nu) that violates Lorentz invariance. We consider the
simplest algebra in which the theta-parameter is promoted to an operator and
Lorentz invariance is preserved. This algebra arises through the contraction of
a larger one for which explicit representations are already known. We formulate
a star product and construct the gauge-invariant Lagrangian for
Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the
theory, while a four-photon coupling exists and leads to a distinctive
phenomenology.
