Document Type : Original Article

Author

‎Department of Physics, Faculty of Science, Shahrekord University, Shahrekord, Iran‎ ‎

Abstract

In the framework of quantum mechanics and based on the non-commutativity between the ‎coordinates in Minkowski space-time, we generalize the geometric non-commutative relation ‎to a space-time other than Minkowski. Using the authority of inserting the unit operator, we ‎exploit the translation operator to derive the Wyle-Moyal star product operator. Up to the first ‎order of translation parameters and by employing the Wyle-Moyal star operator, we find the ‎modified non-commutativity of coordinates relation in terms of geometric structure. The basic ‎premise of this article is that pseudo-Riemannian local homomorphic with Minkowski space-‎time‎‎ are equivalent.
 
 

Highlights

1. P Aschieri, et al,” Non-commutative Spacetimes: Symmetries in Non-commutative Geometry and Field Theory”,  Berlin Heidelberg: Springer, (2009).

2. Connes, M. Marcolli, “Non-commutative Geometry, Quantum Fields and Motives”, London: Academic Press, (1994).

3. N Seiberg and E Witten, JHEP 9909 (1999) 032

4. D J Gross and N A Nekrasov, JHEP 044 (2001)

5. R J Szabo, Phys. Rep. 378 (2003) 207.

6. Fischer, R J Szabo, JHEP 0902 (2009) 031

7. M Chaichian, et al, Eur. Phys. J. C 29 (2003) 413.

8. M M Sheikh-Jabbari, JHEP 9906 (1999) 015.

9. Bertolami, C A D Zarro, Phys. Let. B 673 (2009) 83.

10. A Jafari, Eur. Phys. J. C 73 (2013) 2271

11. L Parker, Phys. Rev. Let. 44 (1980) 1559 and Phys. Rev. D 22 (1980) 1922.

12. C W Misner, et al., “Gravitation” San Francisco: Freeman Publishing Company, (1973), and A Nestrov, Class. Qua. Grav, 16 (1999) 465.

13. J Weber, “General Relativity and Gravitational Waves”, Dover )2004(, (New York: Interscience Publisher Inc., 1961 and M. Maggiore,” Gravitational Waves”, New York: Oxford University Press Inc. )2008).

14. R D'inverno, “Introducing Einstein's Relativity”, New York: Oxford University Press Inc. (1993).

15. B s. DeWitt, Rev. Mod. Phys. 29 (1957) 377.

16. H Kleinert, “Gauge Fields in Condensed Matter”, Singapore: World Scientific Publisher Company, Inc., (1987).

Keywords

1. P Aschieri, et al,” Non-commutative Spacetimes: Symmetries in Non-commutative Geometry and Field Theory”,  Berlin Heidelberg: Springer, (2009).
2. Connes, M. Marcolli, “Non-commutative Geometry, Quantum Fields and Motives”, London: Academic Press, (1994).
3. N Seiberg and E Witten, JHEP 9909 (1999) 032
4. D J Gross and N A Nekrasov, JHEP 044 (2001)
5. R J Szabo, Phys. Rep. 378 (2003) 207.
6. Fischer, R J Szabo, JHEP 0902 (2009) 031
7. M Chaichian, et al, Eur. Phys. J. C 29 (2003) 413.
8. M M Sheikh-Jabbari, JHEP 9906 (1999) 015.
9. Bertolami, C A D Zarro, Phys. Let. B 673 (2009) 83.
10. A Jafari, Eur. Phys. J. C 73 (2013) 2271
11. L Parker, Phys. Rev. Let. 44 (1980) 1559 and Phys. Rev. D 22 (1980) 1922.
12. C W Misner, et al., “Gravitation” San Francisco: Freeman Publishing Company, (1973), and A Nestrov, Class. Qua. Grav, 16 (1999) 465.
13. J Weber, “General Relativity and Gravitational Waves”, Dover )2004(, (New York: Interscience Publisher Inc., 1961 and M. Maggiore,” Gravitational Waves”, New York: Oxford University Press Inc. )2008).
14. R D'inverno, “Introducing Einstein's Relativity”, New York: Oxford University Press Inc. (1993).
15. B s. DeWitt, Rev. Mod. Phys. 29 (1957) 377.
16. H Kleinert, “Gauge Fields in Condensed Matter”, Singapore: World Scientific Publisher Company, Inc., (1987).

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