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We analyse two new versions of \theta-expanded non-commutative quantumelectrodynamics up to first order in \theta and first loop order. In the firstversion we expand the bosonic sector using the Seiberg-Witten map, leaving thefermions unexpanded. In the second version we leave both bosons and fermionsunexpanded. The analysis shows that the Seiberg-Witten map is a fieldredefinition at first order in \theta. However, at higher order in \theta theSeiberg-Witten map cannot be regarded as a field redefinition. We find that theinitial action of any \theta-expanded massless non-commutative QED must includeone extra term proportional to \theta which we identify by loop calculations.Comment: 24 pages, LaTeX, uses the feynmf packag

Quantisation of $\theta$ -expanded non-commutative QED