Document Type : Original Article
Authors
Department of Physics, Urmia University, Urmia, Iran
Abstract
ξ-pseudo Dirac operator has recently been constructed with the help of ξ-pseudo modules and appropriate projectors on AdS2 space. In this article, this operator will be constructed with the help of group theory. For this purpose, firstly, the spin structure of AdS2 space is built and then,with the help of relations related to right and left actions and Maurer-Cartan forms, ξ- pseudo Dirac operator and then its scalar form in, instanton and non-instanton mode is introduced will be and at the end its spectrum is also calculated in different states of this ξ-pseudo operator.
.
Keywords
Main Subjects
- A Connes, “Noncommutative geometry”, Academeic Press, New York (1994).
- A Connes, “Non-commutative Geometry and Physics in Gravitation and Quantization”, Les Houches, Session LVII, Elsevier, Amsterdam (1995).
- U Carow-Watamura and S Watamura, Math. Phys. 183 (1997) 365.
- A P Balachandran, G Immirzi, Rev. D 68 (2003) 065023.
- A P Balachandran and Pramod Padmanabhan, JHEP 09 (2009) 120.
- A P Balachandran, T R Govindarajan and B Ydri, Phys. Lett. A 15 (2000) 1279.
- H Aoki, S Iso and K Nagao, Rev. D 67 (2003) 085005.
- H Fakhri and M Lotfizadeh, JMP 52 (2011) 103508.
- Hossein Fakhri and Ali Imaanpur, High Energy Phys. 03 (2003) 003.
- U Carow-Watamura and S Watamura, J. Mod. Phys. A 13 (1998) 3235.
- H Grosse, C Klimcik and P Presnajder, Math. Phys. 178 (1996) 507.
- H Grosse and P Presnajder, Math. Phys. 33 (1995) 171.
- A Mostafazadeh, Math. Phys. 43 (2002) 205 ; e-print [math-ph/0107001].
- A Mostafazadeh, Math. Phys. 43 (2002) 3944; e-print [math-ph/0203005].
- J Milnor, L’Ens. Math. 9 (1963) 198.
- C J Isham and C N Pope, Physics Letters. B 114 (1982) 137.
- S J Avis and C J Isham, Math. Phys. 72 (1980) 103.
- H R Alagia and C U Sanchez, Union Mathematica Argentina. 32 (1985) 64.
- L Fatibene and M Francaviglia, Acta Physica Polonica B 29 (1998) 915.
- A P Balachandran, Giorgio Immirzi, Joohan Lee and Peter Presnajder, Journal of Mathematical Physics 44 (2003) 4713.
- T Ya Azizov and I S Iokhvidov, “Linear Operators in Spaces with an Indefinite metric”,
Wiley-Interscience, New York (1989); A Dijksma and H. Langer, “Operator Theory and
Ordinary Differential Operators”, in A Bottcher (ed.) et. al., RI, Am. Math. Soc. Fields Institute Monographs,
3 (1996) 75. - Mohammad Enayati, Jean-Pierre Gazeau, Hamed Pejhan and Anzhong Wang, “The de Sitter group and its representations: a window on the notion of de Sitterian elementary systems”, Springer (2022).
- V Bargmann, Ann. Math. 48 (1947)
- Manfred Bohm and Georg Junker, Journal of Mathematical Physics 28 (1987) 1978.
- K Hasebe, Rev. D 78 (2008) 125024.
- A P Balachandran, S Kürkçüoglu, and S Vaidya, “LECTURES ON FUZZY AND FUZZY SUSY PHYSICS”, World Scientific, Singapore (2007).
- R Jackiw and C Rebbi, Rev. Lett. 36 (1976) 1116.
- P Hasenfratz and G ’t Hooft, Rev. Lett. 36 (1976) 1119.
)