2002/11/30 by Zalán Horváth, Zalan Horvath, Olaf Lechtenfeld +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Euclidean geometry #Instanton #Invertible matrix #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Space (punctuation) #Twistor theory #hep-th
paper · pdf · doi:10.1088/1126-6708/2002/12/060
published as JHEP 0212 (2002) 060 · 1+16 pages; v2: typos corrected, published version; v3: eq.(4.16) corrected; v4: eqs. (3.22),(3.24),(3.30),(3.31) corrected
openalex publication_date 2002/12/19 · arxiv created 2003/06/27 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative Euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques.