Lorentz-Invariant Non-Commutative QED

Lorentz-invariant non-commutative QED (NCQED) is constructed such that it should be a part of Lorentz-invariant non-commutative standard model (NCSM), a subject to be treated in later publications. Our NCSM is based on Connes’ observation that the total fermion field in the standard model may be regarded as a bi-module over a flavorcolor algebra. In this paper, it is shown that there 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 the photon field in the same limit, which couples to only four spinors with charges ±2,±1. Following Carlson-Carone-Zobin, our NCQED respects Lorentz invariance employing Doplicher-Fredenhagen-Roberts algebra instead of the usual algebra with constant θ . In the new version θ becomes an integration variable. We show using a simple NC scalar model that the θ integration gives an invariant damping factor instead of the oscillating one to the nonplanar self-energy diagram in the one-loop approximation. Seiberg-Witten map shows that the θ expansion of NCQED generates exotic but wellmotivated derivative interactions beyond QED with allowed charges being only 0,±1,±2. e-mail: [email protected]