Light Propagation in a Background Field for Time-Space Noncommutativity and Axionic Noncommutative QED
We study the low-energy effects of space-time non-commutativity on light propagation in a background electromagnetic field. Contrary to some of the previous claims, we find no polarization rotation for vanishing time-space commutator $[\hat{x}^i,\hat{x}^0]= 0$, although dispersion relation is modified, allowing for propagation faster than the vacuum speed of light. For non-zero $[\hat{x}^i,\hat{x}^0]$, as allowed with a proper quantization, a naive rotation effect is found to be actually absent when physical fields are defined through Seiberg-Witten map. We also consider non-commutative QED weakly coupled to small mass particles such as axions. Non-commutativity is found to dominate the inverse oscillation length, compared to axion mass and QED effects, for mixing particle masses smaller than $10^{-12} eV$. Conventional constraints on axion coupling based on photon-axion transition rates are unmodified, however induced ellipticity is proportional to the non-commutativity squared length scale. This last effect is found to be too small to account for the ellipticity reported by the PVLAS experiment, yet unexplained by conventional QED or axion physics.