The Standard Model on Non-Commutative Space-Time

Abstract

We consider the Standard Model on a non-commutative space and expand the action in the non-commutativity parameter theta. No new particles are introduced, the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard Model. At leading order in theta we find new vertices which are absent in the Standard Model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered.

28 pages, v3: typos corrected, new appendix on alternative kinetic terms for gauge bosons; v4: typos corrected

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