2000/10/07 by É. T. Akhmedov, Emil T. Akhmedov, Philip DeBoer +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1103/physrevd.64.065005
published as Phys.Rev. D64 (2001) 065005 · Latex, 9p, Minor changes, references and clarifications are added
arxiv created 2000/10/07 · openalex publication_date 2001/08/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine the issue of renormalizability of asymptotically free field theories on noncommutative spaces. As an example, we solve the noncommutative O(N) invariant Gross-Neveu model at large N. On commutative space this is a renormalizable model with nontrivial interactions. On the noncommutative space, if we take the translation-invariant ground state, we find that the model is nonrenormalizable. Removing the ultraviolet cutoff yields a trivial noninteracting theory.