Noncommutative Induced Gauge Theories on Moyal Spaces

Understand

Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry.

• Several renormalisable matter field theories that are now identified are briefly reviewed.
• The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined.
• The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented.