Comment on "Dirac equation in the background of the Nutku helicoid metric" [J. Math. Phys. 48, 092301 (2007)]

Birkandan T., Hortacsu M.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.49, sa.5, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Editöre Mektup
  • Cilt numarası: 49 Sayı: 5
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1063/1.2913520
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

The Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on the boundary. This facts explain why we could not find the solution of the system on the boundary in terms of known functions. We make the stability analysis of the helicoid and catenoid cases and end up with an Appendix which gives a new example wherein one encounters a form of the Heun equation. (C) 2008 American Institute of Physics.