We consider the Standard Model on a non-commutative space and expand the action in the non-commutativity parameter θ µν . No new particles are introduced, the structure group is SU (3) × SU (2) × U (1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard Model. At leading order in θ µν 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.

A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincaré group) is replaced by a quantum group. This formalism is demonstrated for the κ-deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable ⋆-product. Fields are elements of this function algebra. The Dirac and Klein-Gordon equation are defined and an action is found from which they can be derived.

We consider a scalar φ 4 theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.

In this article we review the electroweak charged and neutral currents in the Non-Commutative Standard Model (NCSM) and compute the Higgs and Yukawa parts of the NCSM action. With the aim to make the NCSM accessible to phenomenological considerations, all relevant expressions are given in terms of physical fields and Feynman rules are provided. *

We verify explicitly that UV/IR mixing for noncommutative gauge theory can be understood in terms of an induced gravity action, as predicted by the identification [1] of gravity within matrix models of NC gauge theory. More precisely, we obtain the Einstein-Hilbert action by integrating out a scalar field in the adjoint. It arises from the well-known UV/IR mixing of NC gauge theory, which is carefully re-analyzed and interpreted in terms of gravity. The matrix model therefore contains gravity as an IR effect, due to UV/IR mixing.