Exact solution of quantum field theory on noncommutative phase spaces

Edwin Langmann, Richard J. Szabo, Konstantin Zarembo

Research output: Contribution to journalArticlepeer-review

75 Citations (Scopus)


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. © SISSA/ISAS 2004.

Original languageEnglish
Pages (from-to)365-433
Number of pages69
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 1 Jan 2004


  • Matrix Models
  • Non-Commutative Geometry
  • Renormalization Regularization and Renormalons


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