Self-dual and anti-self-dual solutions of discrete Yang-Mills equations on a double complex

2009/09/16 by Volodymyr Sushch, Sushch, Volodymyr
Mathematics · Physics and Astronomy · #39A12 #81T13 #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.0909.3114

openalex publication_date 2009/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a discrete model of the SU(2) Yang-Mills equations on a combinatorial analog of ℝ⁴. Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both techniques of a double complex and the quaternionic approach. Interesting analogies between instanton, anti-instanton solutions of discrete and continual self-dual, anti-self-dual equations are also discussed.

Citations

• Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics

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