Renormalization on the DFR Quantum Spacetime

Abstract

An approach to renormalization of scalar fields on the Doplicher-Fredenhagen-Roberts (DFR) quantum spacetime is presented. The effective non-local theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singularities associated to the non-local kernel that codifies the effects of noncommutativity is analyzed using the tools of microlocal analysis.

arXiv commentFinal version, to appear in Reviews in Mathematical Physics

References in corpus (18)

• String Theory and Noncommutative Geometry
• The quantum structure of spacetime at the Planck scale and quantum fields
• Minimal Length Scale Scenarios for Quantum Gravity
• Space-Time Noncommutative Field Theories And Unitarity
• On the unitarity problem in space/time noncommutative theories
• The causal set approach to quantum gravity
• Multi-Messenger Astrophysics
• Remarks on Time-Space Noncommutative Field Theories
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory
• A smooth introduction to the wavefront set
• Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products
• Spacetime and Fields, a Quantum Texture
• The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes
• Quantum Fields on the Groenewold-Moyal Plane
• On Quantum Spacetime and the horizon problem
• Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence
• Quantum Spacetime and the Universe at the Big Bang, vanishing interactions and fading degrees of freedom