Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces

2003/08/06 by Edwin Langmann, E. Langmann, R. J. Szabo +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1088/1126-6708/2004/01/017

published as JHEP 0401 (2004) 017 · 70 pages AMSTeX

arxiv created 2003/08/06 · openalex publication_date 2004/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinite-dimensional noncommutative algebra.

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