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 $\theta^{\mu \nu}$. No new particles are introduced; the structure group is $SU(3)\times SU(2)\times U(1)$. We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in $\theta^{\mu\nu}$ 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.