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Advances in High Energy Physics
Volume 2015, Article ID 901675, 9 pages
http://dx.doi.org/10.1155/2015/901675
Research Article

On the Thermodynamic Properties of the Spinless Duffin-Kemmer-Petiau Oscillator in Noncommutative Plane

Department of Physics, Guizhou University, Guiyang 550025, China

Received 15 July 2015; Revised 30 September 2015; Accepted 4 October 2015

Academic Editor: Elias C. Vagenas

Copyright © 2015 Zhi Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. N. Kemmer, “Quantum theory of einstein-bose particles and nuclear interaction,” Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, vol. 166, no. 924, pp. 127–153, 1938. View at Publisher · View at Google Scholar
  2. R. J. Duffin, “On the characteristic matrices of covariant systems,” Physical Review, vol. 54, no. 12, p. 1114, 1938. View at Publisher · View at Google Scholar
  3. G. Petiau, “University of Paris thesis,” Académie Royale De Belgique. Classe Des Sciences. Mémoires. Collection, vol. 16, no. 2, p. 1, 1936. View at Google Scholar
  4. V. Y. Fainberg and B. M. Pimentel, “Duffin-Kemmer-Petiau and Klein-Gordon-Fock equations for electromagnetic, Yang-Mills and external gravitational field interactions: proof of equivalence,” Physics Letters A, vol. 271, no. 1-2, pp. 16–25, 2000. View at Publisher · View at Google Scholar
  5. R. F. Guertin and T. L. Wilson, “Noncausal propagation in spin-0 theories with external field interactions,” Physical Review D, vol. 15, no. 6, pp. 1518–1531, 1977. View at Publisher · View at Google Scholar · View at Scopus
  6. B. Vijayalakshmi, M. Seetharaman, and P. M. Mathews, “Consistency of spin-1 theories in external electromagnetic fields,” Journal of Physics A: Mathematical and General, vol. 12, no. 5, pp. 665–677, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  7. I. Boztosun, M. Karakoc, F. Yasuk, and A. Durmus, “Asymptotic iteration method solutions to the relativistic Duffin-Kemmer-Petiau equation,” Journal of Mathematical Physics, vol. 47, no. 6, Article ID 062301, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Boumali, “The eigensolutions of a two-dimensional Kemmer oscillator,” Journal of Physics A: Mathematical and Theoretical, vol. 42, no. 23, Article ID 235301, 2009. View at Publisher · View at Google Scholar
  9. H. Hassanabadi, B. H. Yazarloo, S. Zarrinkamar, and A. A. Rajabi, “Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction,” Physical Review C, vol. 84, no. 6, Article ID 064003, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. L. B. Castro and L. P. de Oliveira, “Remarks on the spin-one duffin-kemmer-petiau equation in the presence of nonminimal vector interactions in (3+1) dimensions,” Advances in High Energy Physics, vol. 2014, Article ID 784072, 8 pages, 2014. View at Publisher · View at Google Scholar
  11. L. B. Castro and A. S. de Castro, “Spinless bosons embedded in a vector Duffin-Kemmer-Petiau oscillator,” Physics Letters A, vol. 375, no. 27, pp. 2596–2600, 2011. View at Publisher · View at Google Scholar
  12. L. B. Castro and A. S. de Castro, “Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations,” Physical Review A, vol. 90, Article ID 022101, 2014. View at Publisher · View at Google Scholar
  13. L. B. Castro, “Quantum dynamics of scalar bosons in a cosmic string background,” The European Physical Journal C, vol. 75, article 287, 2015. View at Publisher · View at Google Scholar
  14. H. S. Snyder, “Quantized space-time,” Physical Review, vol. 71, no. 1, pp. 38–41, 1947. View at Publisher · View at Google Scholar
  15. A. Connes, Noncommutative Geometry, Academic Press, San Diego, Calif, USA, 1994.
  16. T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, “M theory as a matrix model: a conjecture,” Physical Review D, vol. 55, no. 8, pp. 5112–5128, 1997. View at Publisher · View at Google Scholar · View at Scopus
  17. A. E. F. Djemai, “Noncommutative classical mechanics,” International Journal of Theoretical Physics, vol. 43, no. 2, pp. 299–314, 2004. View at Publisher · View at Google Scholar
  18. J. Gamboa, M. Loewe, F. Mendez, and J. C. Rojas, “Noncommutative quantum mechanics,” Physical Review D, vol. 64, no. 6, Article ID 067901, 2001. View at Publisher · View at Google Scholar
  19. J. M. Romero, J. A. Santiago, and J. D. Vergara, “Newton's second law in a non-commutative space,” Physics Letters. A, vol. 310, no. 1, pp. 9–12, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. M. Daszkiewicz and C. J. Walczyk, “Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space,” Physical Review D, vol. 77, no. 10, Article ID 105008, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  21. J. Jing, F. H. Liu, and J. F. Chen, “Classical and quantum mechanics in the generalized non-commutative plane,” EPL, vol. 84, no. 6, Article ID 61001, 2008. View at Publisher · View at Google Scholar
  22. B. Muthukumar and P. Mitra, “Noncommutative oscillators and the commutative limit,” Physical Review D, vol. 66, no. 2, Article ID 027701, 3 pages, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  23. A. Kijanka and P. Kosinski, “Noncommutative isotropic harmonic oscillator,” Physical Review D, vol. 70, no. 12, Article ID 127702, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Jing, S. H. Zhao, J. F. Chen, and Z. W. Long, “On the spectra of noncommutative 2D harmonic oscillator,” The European Physical Journal C, vol. 54, no. 4, pp. 685–690, 2008. View at Publisher · View at Google Scholar
  25. A. Das, H. Falomir, M. Nieto, J. Gamboa, and F. Méndez, “Aharonov-Bohm effect in a class of noncommutative theories,” Physical Review D, vol. 84, no. 4, Article ID 045002, 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. G. Guo, C. Long, Z. Yang, and S. Qin, “DKP oscillator in noncommutative phase space,” Canadian Journal of Physics, vol. 87, no. 9, pp. 989–993, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. H. Hassanabadi, Z. Molaee, and S. Zarrinkamar, “DKP oscillator in the presence of magnetic field in (1+2)-dimensions for spin-zero and spin-one particles in noncommutative phase space,” The European Physical Journal C, vol. 72, article 2217, 2012. View at Publisher · View at Google Scholar
  28. Z.-H. Yang, C.-Y. Long, S.-J. Qin, and Z.-W. Long, “DKP oscillator with spin-0 in three-dimensional noncommutative phase space,” International Journal of Theoretical Physics, vol. 49, no. 3, pp. 644–651, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  29. R. Casana, V. Y. Fainberg, B. M. Pimentel, and J. S. Valverde, “Bose-Einstein condensation and free DKP field,” Physics Letters A, vol. 316, no. 1-2, pp. 33–43, 2003. View at Publisher · View at Google Scholar · View at Scopus
  30. M. H. Pacheco, R. R. Landim, and C. A. S. Almeida, “One-dimensional Dirac oscillator in a thermal bath,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 311, no. 2-3, pp. 93–96, 2003. View at Publisher · View at Google Scholar · View at Scopus
  31. M. H. Pacheco, R. V. Maluf, C. A. S. Almeida, and R. R. Landim, “Three-dimensional Dirac oscillator in a thermal bath,” EPL, vol. 108, no. 1, Article ID 10005, 2014. View at Publisher · View at Google Scholar · View at Scopus
  32. A. Boumali and H. Hassanabadi, “The thermal properties of a two-dimensional Dirac oscillator under an external magnetic field,” The European Physical Journal Plus, vol. 128, article 124, 2013. View at Publisher · View at Google Scholar
  33. H. Hassanabadi, S. S. Hosseini, A. Boumali, and S. Zarrinkamar, “The statistical properties of Klein-Gordon oscillator in noncommutative space,” Journal of Mathematical Physics, vol. 55, no. 3, Article ID 033502, 2014. View at Publisher · View at Google Scholar · View at Scopus
  34. S. Hassanabadi and M. Ghominejad, “The statistical properties of spin-one DKP oscillator under an external magnetic field in noncommutative space,” Advances in High Energy Physics, vol. 2014, Article ID 185169, 7 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  35. Y. Nedjadi and R. C. Barrett, “The Duffin-Kemmer-Petiau oscillator,” Journal of Physics A: Mathematical and General, vol. 27, no. 12, pp. 4301–4315, 1994. View at Publisher · View at Google Scholar
  36. Y. Nedjadi and R. C. Barrett, “On the properties of the Duffin-Kemmer-Petiau equation,” Journal of Physics G: Nuclear and Particle Physics, vol. 19, no. 1, pp. 87–98, 1993. View at Publisher · View at Google Scholar
  37. G. E. Andrews, R. Askey, and A. Roy, Special Functions, Cambridge University Press, Cambridge, UK, 1999.
  38. A. Boumali, “The one-dimensional thermal properties for the relativistic harmonic oscillators,” Electronic Journal of Theoretical Physics, vol. 12, no. 32, pp. 121–130, 2015. View at Google Scholar
  39. A. Boumali, “Thermal properties of the one-dimensional Duffin-Kemmer-Petiau oscillator using Hurwitz zeta function,” Zeitschrift für Naturforschung A, vol. 70, no. 10, pp. 867–874, 2015. View at Publisher · View at Google Scholar
  40. A. J. Silenko, “Quantum-mechanical description of spin-1 particles with electric dipole moments,” Physical Review D, vol. 87, no. 7, Article ID 073015, 2013. View at Publisher · View at Google Scholar
  41. A. J. Silenko, “High precision description and new properties of a spin-1 particle in a magnetic field,” Physical Review D, vol. 89, no. 12, Article ID 121701, 2014. View at Publisher · View at Google Scholar
  42. H. B. Nielsen and M. Ninomiya, “Dirac sea for bosons. 1—formulation of negative energy sea for bosons,” Progress of Theoretical Physics, vol. 113, no. 3, pp. 603–624, 2005. View at Publisher · View at Google Scholar
  43. H. B. Nielsen and M. Ninomiya, “Dirac Sea for Bosons. II—study of the naive vacuum theory for the toy model world prior to filling the negative energy sea,” Progress of Theoretical Physics, vol. 113, no. 3, pp. 625–643, 2005. View at Publisher · View at Google Scholar
  44. M.-A. Dariescu and C. Dariescu, “Persistent currents and critical magnetic field in planar dynamics of charged bosons,” Journal of Physics Condensed Matter, vol. 19, no. 25, Article ID 256203, 2007. View at Publisher · View at Google Scholar · View at Scopus