Lorentz-Invariant Non-Commutative QED

Lorentz-invariant non-commutative QED (NCQED) is constructed such that itshould be a part of Lorentz-invariant non-commutative standard model (NCSM), asubject to be treated in later publications. Our NCSM is based on Connes'observation that the total fermion field in the standard model may be regardedas a bi-module over a flavor-color algebra. In this paper, it is shown thatthere exist two massless gauge fields in NCQED which are interchanged by $C'$transformation. Since $C'$ is reduced to the conventional charge conjugation$C$ in the commutative limit, the two gauge fields become identical to thephoton field in the same limit, which couples to only four spinors with charges$\pm 2,\pm 1.$ Following Carlson-Carone-Zobin, our NCQED respects Lorentzinvariance employing Doplicher-Fredenhagen-Roberts' algebra instead of theusual algebra with constant $\theta^{\mu\nu}$. In the new version$\theta^{\mu\nu}$ becomes an integration variable. We show using a simple NCscalar model that the $\theta$ integration gives an {\it invariant} dampingfactor instead of the oscillating one to the nonplanar self-energy diagram inthe one-loop approximation. Seiberg-Witten map shows that the $\theta$expansion of NCQED generates exotic but well-motivated derivative interactionsbeyond QED with allowed charges being only $0, \pm 1, \pm 2$.Comment: LaTeX file, 27 page