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

• VOLODYMYR SUSHCH ^[1]
  1. [1] Koszalin University of Technology

     Koszalin University of Technology

     Koszalin, Polonia

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 3, 2010, págs. 99-120
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000300007
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • ATIYAH, M.F. (1979). Geometry of Yang-Mills Fields: Lezione Fermiane. Scuola Normale Superiore Pisa.
  • DE BEAUCÉ, V,SEN, S,SEXTON, J.C. (2004). Chiral dirac fermions on the lattice using geometric discretisation. Nucl. Phys. B (Proc. Suppl....
  • BELAVIN, A,POLYAKOV, A,SCHWARTZ, A,TYUPKIN, Y. (1976). Pseudoparticle solutions of the Yang-Mills equations. Phys. Lett. B. 59. 86-87
  • CASTELLANI, L,PAGANI, C. (2002). Finite Group Discretization of Yang-Mills and Einstein Actions. Annals of Physics. 297. 295-314
  • CORRIGAN, E,FAIRLIE, D.B. (1977). Scalar field theory and exact solutions to a classical SU(2)-gauge theory. Phys. Lett. B. 67. 69-71
  • DEZIN, A.A. (1995). Multidimensional Analysis and Discrete Models. CRC Press. Boca Raton.
  • DEZIN, A.A. (1993). Models generated by the Yang-Mills equations, Differentsial’nye Uravneniya: 29 (1993), no. 5, 846-851. English translation...
  • FREED, D,UHLENBECK, K. (1984). Instantons and Four-Manifolds. Springer-Verlag.
  • DE FORCRAND, PH,JAHN, O. (2003). Comparison of SO(3) and SU(2) lattice gauge theory. Nuclear Physics B. 651. 125-142
  • GONZALEZ-ARROYO, A,MONTERO, A. (1998). Self-dual vortex-like configurations in SU(2) Yang-Mills theory. Physics Letters B. 442. 273-278
  • JACKIW, R,NOHL, C,REBBI, C. (1977). Conformal properties of pseudo-particle configurations. Phys. Rev. 150. 1642-1646
  • KAMATA, M,NAKAMULA, A. (1999). One-parameter family of selfdual solutions in classical Yang-Mills theory. Physics Letters B. 463. 257-262
  • NAKAMULA, A. (2001). Selfdual solution of classical Yang-Mills fields through a q-analog of ADHM construction. Reports On Mathematical Physics....
  • NASH, C,SEN, S. (1989). Toplogy and Geometry for Physicists. Acad. Press. London.
  • NISHIMURA, J. (1997). Four-dimensional N = 1 supersymmetric Yang-Mills theory on the lattice without fine-tuning. Phys. Lett.B. 406. 215-218
  • SEILER, E. (1982). Gauge theories as a problem of constructive quantum field theory and statistical mechanics. Springer-Verlag.
  • SEN, S,SEN, S,SEXTON, J.C,ADAMS, D. (2000). A geometric discretisation scheme applied to the Abelian Chern-Simons theory. Phys. Rev. E. 61....
  • SHABANOV, S. (2001). Infrared Yang-Mills theory as a spin system: A lattice approach. Phys. Lett.B. 522. 201-209
  • SUSHCH, V. (1997). Gauge-invariant discrete models of Yang-Mills equations: Mat. Zametki. 61. 742-754
  • SUSHCH, V. (2004). Discrete model of Yang-Mills equations in Minkowski space. Cubo A Math. Journal. 6. 35-50
  • SUSHCH, V. (2006). A gauge-invariant discrete analog of the Yang-Mills equations on a double complex. Cubo A Math. Journal. 8. 61-78