CUBO A Mathematical Journal Vol.12, N°03, (99–120). October 2010

 

Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex

 

VOLODYMYR SUSHCH

Koszalin University of Technology, Sniadeckich 2, 75-453 Koszalin, Poland email: volodymyr.sushch@tu.koszalin.pl

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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.

Key words and phrases: Yang-Mills equations, self-dual and anti-self-dual equations, instantons and anti-instantons, difference equations.

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RESUMEN

Estudiamos el modelo discreto de las ecuaciones de Yang-Mills SU(2) sobre un análogo combinatório de R4. Soluciones auto-dual y anti-auto-dual para las ecuaciones discretas de Yang-Mills son construidas. Para obtener estas soluciones usamos las técnicas de doble complejo y abordage cuaternionico. Interesantes analogías entre soluciones instantones y anti-instantones de ecuaciones discretas y continuas auto-dual y anti-auto-dual son discutidas.

Math. Subj. Class.: 81T13, 39A12.

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