Lorentz-Invariant Non-Commutative QED(Particles and Fields)

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Lorentz-invariant non-commutative QED (NCQED) is constructed so as to be a part of the 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 can be regarded as a bi-module over a flavor-color algebra. In this paper, it is shown that there exist two massless gauge fields in NCQED that are interchanged by the C′ transformation. Since C′ is reduced to the conventional charge conjugation C in the commutative limit, in the same limit, the two gauge fields become identical to the photon field which couples to only four spinors, with charges ±2, ±1. Following Carlson, Carone and Zobin, our NCQED respects Lorentz invariance, employing the Doplicher-Fredenhagen-Roberts algebra instead of the usual algebra with constant θ^μν. In the new version, θ^μν becomes an integration variable. We show, using a simple NC scalar model, that the θ integration yields an invariant damping factor instead of the oscillating one in the nonplanar self-energy diagram in the one-loop approximation. The Seiberg-Witten map shows that the θ expansion of NCQED generates exotic but well-motivated derivative interactions beyond QED, with allowed charges being only 0, ±1, ±2.
理論物理学刊行会の論文
2002-12-25