Twisted Poincaré Invariant Quantum Field Theories

Abstract

It is by now well known that the Poincaré group acts on the Moyal plane with a twisted coproduct. Poincaré invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincaré action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the Poincaré group, ensuring also the invariance of the S-matrix under the twisted action of the group . A significant new contribution here is the construction of the Poincaré generators using quantum fields.

17 pages, JHEP style

References in corpus (4)

• A Gravity Theory on Noncommutative Spaces
• Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
• Quantum Fields with Noncommutative Target Spaces
• S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance

Cited by in corpus (7)

• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Quantum Fields on the Groenewold-Moyal Plane
• Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
• Twisted Poincare Invariance, Noncommutative Gauge Theories and UV-IR Mixing
• S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance
• Noncommutative fields and actions of twisted Poincare algebra
• Duality and Braiding in Twisted Quantum Field Theory