Noncommutative QFT and Renormalization

Abstract

Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to ${\varphi }^3$ models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $\theta$-deformed space and derive noncommutative gauge field actions.

To appear in the proceedings of the Workshop "Noncommutative Geometry in Field and String Theory", Corfu, 2005 (Greece)

Cited by in corpus (10)

• Noncommutative Induced Gauge Theory
• Induced Gauge Theory on a Noncommutative Space
• Noncommutative D=4 gravity coupled to fermions
• On the vacuum states for noncommutative gauge theory
• Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
• Noncommutative Induced Gauge Theories on Moyal Spaces
• Heat Trace Asymptotics on Noncommutative Spaces
• On space-time noncommutative theories at finite temperature
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• Induced Gauge Theory on a Noncommutative Space