Exact Solution of Noncommutative Field Theory in Background Magnetic Fields

Abstract

We obtain the exact non-perturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes non-locally interacting charged particles in a background magnetic field. It is an exactly solvable quantum field theory which has non-trivial 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.

9 Pages AMSTeX; Typos corrected

References in corpus (12)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Introduction to M(atrix) theory and noncommutative geometry
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
• The Multicritical Kontsevich-Penner Model
• Interacting fermions on noncommutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions
• Quantum Aspects of GMS Solutions of Noncommutative Field Theory and Large N Limit of Matrix Models
• Running couplings and triviality of field theories on non-commutative spaces
• Quantum Field Dynamics in a Uniform Magnetic Field: Description using Fields in Oblique Phase Space

Cited by in corpus (32)

• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Noncommutative Induced Gauge Theory
• Non-commutative Renormalization
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• On the vacuum states for noncommutative gauge theory
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• The Fuzzy Disc
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Superfield theory and supermatrix model
• Lectures on Matrix Field Theory I
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Duality covariant quantum field theory on noncommutative Minkowski space
• Chiral Bosons in Noncommutative Spacetime
• Noncommutative Induced Gauge Theories on Moyal Spaces
• One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• Exact solution of matricial ${\Phi }_2^3$ quantum field theory
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• On the Renormalization of Non-Commutative Field Theories
• Translation-Invariant Noncommutative Renormalization
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• On the Effective Action of Noncommutative Yang-Mills Theory
• Matrix Model Fixed Point of Noncommutative Phi-Four
• Exactly solvable models for 2D correlated fermions
• Why Renormalizable NonCommutative Quantum Field Theories?
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• $U(N)$ Yang-Mills in non-commutative space time
• Symmetries of field theories on the non-commutative plane
• Wilson RG of Noncommutative ${\Phi }_4^4$
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Non-commutative geometry and exactly solvable systems