Two-Dimensional Vector Boson Oscillator

We introduce two-dimensional vector boson oscillator (VBO) by using the generalized vector boson equation that derived as an excited state from the canonical quantization of classical spinning particle with Zitterbewegung. We write the relativistic vector boson equation (VBE) and introduce the oscillator coupling through non-minimal substitutions. This form of the equation is linear in both momentum and coordinate. The corresponding equation gives a set of coupled equations. By solving these equations we obtain an exact energy spectrum for two-dimensional VBO. This energy spectrum includes spin coupling and shows that the oscillator frequency depends on the spin of the vector boson. According to these results, we discuss several properties of the two-dimensional VBO.

Keywords:

Relativistic Quantum Mechanics, Quantum Oscillator Vector Boson.,

PDF

___

[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.