Galois quantum systems, irreducible polynomials and Riemann surfaces

Journal of Mathematical Physics

Volumn 47, Issue 9, 2006, Pages

  Vourdas, A ^a  

^a UNIVERSITY OF BRADFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749351484     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2345111     Document Type: Article

References (40)

1. H. Weyl, Theory of Groups and Quantum Mechanics (Dover, New York, 1950).
2. J. Schwinger, Proc. Natl. Acad. Sci. U.S.A. 46, 570 (1960);
3. Quantum Kinematics and Dynamics (Benjamin, New York, 1970).
4. A. Vourdas, Rep. Prog. Phys. 67, 267 (2004).
5. J. W. P. Hirschfeld, Projective Geometries Over Finite Fields (Oxford University Press, Oxford, 1979);
6. L. M. Batten, Combinatorics of Finite Geometries (Cambridge University Press, Cambridge, 1997);
7. R. Lidl and H. Niederreiter, Finite Fields (Cambridge University Press, Cambridge, 1997);
8. A. Terras, Fourier Analysis on Finite Groups and Applications (Cambridge University Press, Cambridge, 1999).
9. A. Vourdas, J. Phys. A 29, 4275 (1996).
10. M. Neuhauser, J. Lie Theory 12, 15 (2002).
11. A. Vourdas, J. Phys. A 38, 8453 (2005);
12. Acta Appl. Math (quant-phys/0605054).
13. W. Wootters, Ann. Phys. (N.Y.) 176, 1 (1987);
14. W. Wootters and B. D. Fields, Ann. Phys. (N.Y.), ibid. 191, 363 (1989);
15. K. Gibbons, M. J. Hoffman, and W. Wootters, Phys. Rev. A 70, 062101 (2004).
16. S. Bandyopadhyay, P. O. Boykin, V. Roychowdhury, and F. Vatan, Algorithmica 34, 512 (2002).
17. A. O. Pittenger and M. H. Rubin, Linear Algebr. Appl. 390, 255 (2004);
18. J. Phys. A 38, 6005 (2005).
19. A. Klappenecker and M. Rotteler, Lect. Notes Comput. Sci. 2948, 137 (2004).
20. P. Wocjan and T. Beth, Quantum Inf. Comput. 5, 181 (2005).
21. A. Klimov, L. Sanchez-Soto, and H. de Guise, J. Phys. A 38, 2747 (2005);
22. J. Opt. B: Quantum Semiclassical Opt. 7, 283 (2005);
23. J. L. Romero, G. Bjork, A. B. Klimov, and L. L. Sanchez-Soto, Phys. Rev. A 72, 062310 (2005).
24. M. Saniga, M. Planat, and H. Rosu, J. Opt. B: Quantum Semiclassical Opt. 6, L19 (2004);
25. J. Phys. A 39, 435 (2006).
26. M. R. Kibler and M. Planat, Int. J. Mod. Phys. B 20, 1802 (2006);
27. M. R. Kibler and M. Planat, Int. J. Mod. Phys. B, 20, 1792 (2006);
28. T. Durt, J. Phys. A 38, 5267 (2005).
29. S. Colin, J. Corbett, T. Durt, and D. Gross, J. Opt. B; Quantum Semiclassical Opt. 7, S778 (2005).
30. E. F. Calvao, Phys. Rev. A 71, 042302 (2005).
31. I. Bengtsson and A. Ericsson, Open Syst. Inf. Dyn. 12, 107 (2005).
32. B. G. Englert and Y. Aharonov, Phys. Lett. A 284, 1 (2001).
33. A. Hayashi, M. Horibe, and T. Hashimoto, Phys. Rev. A 71, 052331 (2005).
34. T. Durt, Int. J. Mod. Phys. B 20, 1742 (2006).
35. A. Asikhmin and E. Knill, IEEE Trans. Inf. Theory 47, 3065 (2001).
36. A. Vourdas. Phys. Rev. A 65, 042321 (2002);
37. J. Phys. A 37, 3305 (2004).
38. E. Reyssat in From Number Theory to Physics, edited by M. Waldschmidt, P. Moussa, J. M. Louck, and C. Itzykson (Springer, Berlin, 1992).
39. A. Vourdas, J. Phys. A 39, R65 (2006).
40. A. Vourdas, J. Math. Phys. 35, 2687 (1994).