Exact solution of noncommutative field theory in background magnetic fields

2003/03/24 by Edwin Langmann, E. Langmann, R. J. Szabo +3 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1016/j.physletb.2003.07.020

published as Phys.Lett. B569 (2003) 95-101 · 9 Pages AMSTeX; Typos corrected

arxiv created 2003/03/24 · openalex publication_date 2003/08/12 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We obtain the exact nonperturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes nonlocally interacting charged particles in a background magnetic field. It is an exactly solvable quantum field theory which has nontrivial interactions only when it is defined with a finite ultraviolet cutoff. We propose that small perturbations of this theory can produce solvable models with renormalizable interactions.

Citations

• A planar diagram theory for strong interactions

Cited by

• Non-commutative geometry and exactly solvable systems
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces