Two-Dimensional Vector Boson Oscillator

We introduce two-dimensional vector boson oscillator by using the generalized vector bosonequation that derived as an excited of Zitterbewegung. We write the relativistic vector bosonequation for a relativistic spin-1 particle and introduce the oscillator coupling via non-minimalsubstitutions. The corresponding equation gives a set of equations. By solving this equation setwe obtain the components of the corresponding symmetric spinor and accordingly obtain theenergy eigen-values for two-dimensional vector boson oscillator. This energy spectrum showsthat the oscillator frequency couples with the spin of vector field in question and accordinglywe discuss the results.

___

[1] M. Moshinsky, A. Szczepaniak, “The Dirac oscillator.” Journal of Physics A: Mathematical and General, vol. 22, no. 17, pp. L817-L819, 1989.

[2] S. Bruce and P. Minning, “The KleinGordon oscillator,” Il Nuovo Cimento A, vol. 106, no. 5, pp. 711–713, 1993.

[3] N. Debergh, J. Ndimubandi, and D. Strivay, “On relativistic scalar and vector mesons with harmonic oscillator - like interactions,” Zeitschrif fur Physik C Particles and Fields ¨ , vol. 56, pp. 421–425, 1992.

[4] Y. Nedjadi and R. C. Barrett, “The DufnKemmer-Petiau oscillator,” Journal of Physics A: Mathematical and General, vol. 27, no. 12, pp. 4301–4315, 1994.

[5] A. Guvendi, S. Zare and H. Hassanabadi “Vector boson oscillator in the spiral dislocation spacetime”, The European Physical Journal A, vol. 57, no. 6, pp. 1-6, 2021.

[6] A.Guvendi, and H. Hassanabadi “Relativistic vector Bosons with Nonminimal coupling in the Spinning Cosmic String Spacetime”, The European Physical Journal A, vol. 62, no. 3, pp. 1-8, 2021.

[7] J. Benitez, R. P. Martnez y Romero, H. N. Nuez-Y ´ epez, and A. ´ L. Salas-Brito, “Solution and hidden supersymmetry of a Dirac oscillator,” Physical Review Letters, vol. 64, no. 14, pp. 1643–1645, 1990.

[8] M. Moreno and A. Zentella, “Covariance, CPT and the FoldyWouthuysen transformation for the Dirac oscillator,” Journal of Physics A: Mathematical and General, vol. 22, no. 17, pp. L821, 1989.

[9] A. Guvendi, Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction. European Physical Journal C, vol. 81, no. 2, pp.1-7, 2021.

[10] A. Guvendi, “Dynamics of a composite system in a point source-induced spacetime”, International Journal of modern Physics A, vol. 36, no. 19, pp.2150144, 2021.

[11] A. Bermudez, M.A. Martin-Delgado, E. Solano, Exact mapping of the 2+ 1 Dirac oscillator onto the Jaynes-Cummings model: Iontrap experimental proposal, Physical Review A, vol.76, no. 4, pp. 041801, 2007.

[12] Y. Luo, Y. Cui, Z. Long, and J. Jing, “2+1 Dimensional Noncommutative Dirac Oscillator and (Anti)-JaynesCummings Models,” International Journal of Theoretical Physics, vol. 50, no. 10, pp. 2992–3000, 2011.

[13] Y. Chargui and A. Dhahbi, “On the qdeformed Dirac oscillator in (2+1)- dimensional space–time”, Annals of Physics, vol.428, pp. 168430, 2021.

[14] M. H. Pacheco, R. R. Landim and C. A. S. Almeida, “One-dimensional Dirac oscillator in a thermal bath,” Physics Letters A, vol. 311, no. 2-3. pp 93-96, 2003.

[15] M. Moshinsky, Y.F. Smirnov, “The Harmonic Oscillator in Modern Physics”, vol. 9, pp. 414, CRC Press, Boca Raton, 1996.

[16] M. Moshinsky, G. Loyola, “Barut equation for the particle antiparticle system with a Dirac oscillator interaction”. Found. Phys. Vol.23, 197–210, 1993.

[17] J. Carvalho, C. Furtado and F. Moreas, “Dirac oscillator interacting with a topological defect,” Physical Review A, vol. 84, no. 3. pp. 032109, 2011.

[18] M. M. Cunha, H. S. Dias, and E. O. Silva, “Dirac oscillator in a spinning cosmic string spacetime in external magnetic fields: Investigation of the energy spectrum and the connection with condensed matter” Physical Review D, vol.102, no.10, pp. 105020, 2020.

[19] A. Boumali and N. Messai, “Klein–Gordon oscillator under a uniform magnetic field in cosmic string space–time,” Canadian Journal of Physics, vol. 92, no. 11, pp. 1460–1463, 2014.

[20] K. Bakke and C. Furtado, “On the KleinGordon oscillator subject to a Coulombtype potential,” Annalen der Physik, vol. 355, pp. 48–54, 2015.

[21] R. L. L. Vitória, C. Furtado, and K. Bakke, “On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein-Gordon oscillator and the Coulomb potential,” Annals of Physics, vol. 370, pp. 128–136, 2016.

[22] F. Ahmed, “The Klein-Gordon oscillator in (1+2)-dimensions Gurses space-time backgrounds,” Annals of Physics, vol. 404, pp. 1-9, 2019.

[23] F. Ahmed, “The generalized Klein-- Gordon oscillator in the background of cosmic string space-time with a linear potential in the Kaluza--Klein theory,” The European Physical Journal C, vol. 80, pp. 1- 12, 2020.

[24] L. Zhong, H. Chen, Z. W. Long, C. Y. Long, and H. Hassanabadi, “The study of the generalized Klein--Gordon oscillator in the context of the Som--Raychaudhuri space--time,”International Journal of Modern Physics A, pp. 2150129, 2021.

[25] R. J. Duffin, “On the characteristic matrices of covariant systems,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 54, no. 12, pp. 1114, 1938.

[26] N. Kemmer, “The particle aspect of meson theory,” Proceedings of the Royal Society A Mathematical, Physical and Engineering Sciences, vol. 173, no. 952, pp. 91–116, 1939.

[27] G. Petiau, “Contribution à la théorie des équations d’ondes corpusculaires,” Mémories de l’Académie Royale de Belgique, Classe des, vol. 8, no. 2, pp. 16, 1936.

[28] A Boumali, L Chetouani, H Hassanabadi, Canadian Journal of Physics, “Twodimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field “vol. 91, no.1, pp. 1-11, 2013.

[29] M. Falek, M. Merad, and M. Moumni "Bosonic oscillator under a uniform magnetic field with Snyder-de Sitter algebra" Journal of Mathematical Physics, vol. 60, no.1, pp. 013505, 2019.

[30] I.S. Gomez and E. S. Santos and O. Abla, Physics Letters A , “Splitting frequency of the (2 + 1)-dimensional Duffin-KemmerPetiau oscillator in an external magnetic field “, vol. 384, no.27, pp. 126706, 2020.

[31] 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 Teoretical Physics, vol. 49, no. 3, pp. 644–651, 2010.

[32] M. Falek and M. Merad, “DKP oscillator in a non-commutative space,” Communications in Teoretical Physics, vol. 50, no. 3, pp. 587–592, 2008.

[33] M. Falek and M. Merad, “Bosonic oscillator in the presence of minimal length,” Journal of Mathematical Physics, Journal of Mathematical Physics, vol.50, no.2, pp. 023508, 2009.

[34] B. Hamil, and M. Merad and T. Birkandan, ”The Duffin-Kemmer-Petiau oscillator in the presence of minimal uncertainty in momentum” , Physica Scripta, vol. 95, no.7, pp. 075309, 2020.

[35] A. O. Barut, “Excited states of zitterbewegung,” Physics Letters B, vol. 237, no. 3, pp. 436-439, 1990.

[36] N. Ünal, “A simple model of the classical zitterbewegung: photon wave function”, Foundations of Physics, vol. 27, no. 5. pp 731-746, 1997.

[37] N. Ünal, “Path Integral Quantization of a Spinning Particle” Foundations of Physics, vol. 28 no.5, pp.755–762. 1998.

[38] A. Guvendi, R. Sahin and Y. Sucu, “Exact solution of an exciton energy for a monolayer medium,” Scientific Reports, vol. 9, no. 1. pp 1-6, 2019.

[39] A. Guvendi and Y. Sucu, “An interacting fermion-antifermion pair in the spacetime background generated by static cosmic string,” Physics Letters B, vol. 811, no. 135960. pp 135960, 2020.

[40] M. Dernek and S. G. Doğan and Y. Sucu and N. Ünal, “Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime,” Turkish Journal of Physics, vol. 42, no. 5. pp 509-526, 2018.

[41] Y. Sucu and C. Tekincay, “Photon in the Earth-ionosphere cavity: Schumann resonances,” Astrophysics and Space Science, vol. 364, no. 4. pp 1-7, 2019.

[42] G. Gecim and Y. Sucu, “The GUP effect on tunneling of massive vector bosons from the 2+1 dimensional blackhole,” Advances in High Energy Physics, vol. 2018, no. 8. pp 1- 8, 2018.

[43] Y. Sucu and N. Ünal, “Vector bosons in the expanding universe,” The European Physical Journal C, vol. 44, no. 2. pp 287- 291, 2005.

[44] R. E. Kozack, B. C. Clark, S. Hama, V. K. Mishra, R. L. Mercer, and L. Ray, “Spinone Kemmer-Duffin-Petiau equations and intermediate-energy deuteron-nucleus scattering,” Physical Review C, vol. 40, no. 5, pp. 2181–2194, 1989.

[45] M. Hosseinpour, H. Hassanabadi and F. M. Andrade, “The DKP oscillator with a linear interaction in the cosmic string space-time,” The European Physical Journal C, vol. 78, no. 2. pp 1-7, 2018.

[46] A. Guvendi and S. G. Doğan, “Relativistic Dynamics of Oppositely charged Two Fermions Interacting with External Uniform Magnetic Field,” Few-Body Systems, vol. 62, no. 1. pp 1-8, 2021.

[47] A. Guvendi, R. Sahin and Y. Sucu, “Binding energy and decaytime of exciton in dielectric medium,” The European Physical Journal B, vol. 94, no. 1. pp 1-7, 2021.

[48] C. Tezcan and R. Sever, “A General Approach for the Exact Solution of the Schrodinger Equation” Int. J. Theor. Phys. vol. 48, no. 2, pp. 337, 2009.

[49] A.F. Nikiforov and V.B. Uvarov, “Special Functions of Mathematical Physics”, Birkhauser, Basel vol.205, pp. 427, 1988.

[50] A. Boumali, “One-dimensional thermal properties of the Kemmer oscillator,” Physica Scripta, vol. 76, no. 6. pp 669, 2007.
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi-Cover
  • ISSN: 1301-4048
  • Yayın Aralığı: Yılda 6 Sayı
  • Başlangıç: 1997
  • Yayıncı: Sakarya Üniversitesi Fen Bilimleri Enstitüsü