Peter Schupp

Gauge theory on noncommutative spaces

Abstract. We introduce a formulation of gauge theory on noncommutative spaces based on the notion of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases.

A gravity theory on noncommutative spaces

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter ?. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra, a covariant tensor calculus is constructed and all the concepts such as metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a ?-deformed Einstein?Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in ?.

Construction of non-Abelian gauge theories on noncommutative spaces

Abstract. We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.

Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces

Abstract. An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.

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

Nonabelian noncommutative gauge theory via noncommutative extra dimensions

\theta^{\mu \nu}

Noncommutative Yang-Mills from equivalence of star products

. No new particles are introduced; the structure group is

Noncommutative gauge theory for Poisson manifolds

SU(3)\times SU(2)\times U(1)

Membrane sigma-models and quantization of non-geometric flux backgrounds

. We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in

The

\theta^{\mu\nu}