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Relativistic free fermions in an elastic medium with screw dislocations

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Abstract

We study the Dirac equation for free fermions in an elastic medium with a linear topological defect or distortion analogous to a screw dislocation. We obtain its wave functions for free particle and the corresponding energy spectrum, as well as the fermionic current density. Furthermore, we provide the energy–momentum density for four well-known forms: Einstein, Landau–Lifshitz, Papapetrou and Bergmann–Thomson.

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References

  1. 1.

    R.A. Puntigam, H.H. Soleng, Class. Quantum Grav. 14, 1129 (1997). https://doi.org/10.1088/0264-9381/14/5/017

  2. 2.

    M.O. Katanaev, I.V. Volovich, Ann. Phys. 216, 1 (1992). https://doi.org/10.1016/0003-4916(52)90040-7

  3. 3.

    A.V.D.M. Maia, K. Bakke, On an electron in an elastic medium with a spiral dislocation. arXiv: 1907.09005

  4. 4.

    J. Sólyom, Fundamentals of the Physics of Solids, Volume 1: Structure and Dynamics, vol. 1 (Springer, Berlin, 2007). ISBN: 978-3-540-72599-2

  5. 5.

    A.E. Romanov, V.I. Vladimiro, Phys. Status Solidi (a) 78, 11 (1983). https://doi.org/10.1002/pssa.2210780102

  6. 6.

    W.C.F. da Silva, K. Bakke, Eur. Phys. J. Plus 134, 131 (2019). https://doi.org/10.1140/epjp/i2019-12556-7

  7. 7.

    G. de A Marques, C. Furtado, V.B. Bezerra, F. Moraes, J. Phys. A: Math. Gen. 5945, 34 (2001). https://doi.org/10.1088/0305-4470/34/30/306

  8. 8.

    C. Furtado, F. Moraes, Europhys. Lett. 45, 279 (1999). https://doi.org/10.1209/epl/i1999-00159-8

  9. 9.

    A.L.S. Netto, C. Furtado, J. Phys.: Condens. Matter 20, 125209 (2008). https://doi.org/10.1088/0953-8984/20/12/125209

  10. 10.

    C. Filgueiras, M. Rojas, G. Aciole, E.O. Silva, Phys. Lett. A 380, 3847 (2016). https://doi.org/10.1016/j.physleta.2016.09.025

  11. 11.

    C. Furtado, V.B. Bezerra, F. Moraes, Phys. Lett. A 289, 160 (2001). https://doi.org/10.1016/S0375-9601(01)00615-6

  12. 12.

    A.L. Silva Netto, C. Chesman, C. Furtado, Phys. Lett. A 372, 3894 (2008). https://doi.org/10.1016/j.physleta.2008.02.060

  13. 13.

    L. Dantas, C. Furtado, A.L. Silva Netto, Phys. Lett. A 379, 11 (2015). https://doi.org/10.1016/j.physleta.2014.10.016

  14. 14.

    C. Furtado, F. Moraes, J. Phys. A: Math. Gen. 33, 5513 (2000). https://doi.org/10.1088/0305-4470/33/31/306

  15. 15.

    M.J. Bueno, C. Furtado, K. Bakke, Physica B 496, 45 (2016). https://doi.org/10.1016/j.physb.2016.05.026

  16. 16.

    K. Bakke, Physica B: Condensed Matter 537, 346 (2018). https://doi.org/10.1016/j.physb.2018.02.040

  17. 17.

    C. Filgueiras, E.O. Silva, Phys. Lett. A 379, 2110 (2015). https://doi.org/10.1016/j.physleta.2015.06.035

  18. 18.

    W.C.F. da Silva, K. Bakke, Eur. Phys. J. C 79, 559 (2019). https://doi.org/10.1140/epjc/s10052-019-7073-0

  19. 19.

    R.L.L. Vitória, K. Bakke, Eur. Phys. J. C 78, 175 (2018). https://doi.org/10.1140/epjc/s10052-018-5658-7

  20. 20.

    R.L.L. Vitória, K. Bakke, Eur. Phys. J. Plus 133, 490 (2018). https://doi.org/10.1140/epjp/i2018-12310-9

  21. 21.

    M. Sharif, K. Nazir, Braz. J. Phys. 38, 156 (2008). https://doi.org/10.1590/S0103-97332008000100028

  22. 22.

    I. Radinschi, F. Rahaman, T. Grammenos, S. Islam, Adv. High Energy Phys. 2016, 9049308 (2016). https://doi.org/10.1155/2016/9049308

  23. 23.

    A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 778 (1915)

  24. 24.

    A. Trautman, in Gravitation: An Introduction to Current Research, ed. by L. Witten (Wiley, New York, 1962), p. 169. ISBN: 978-1114291669

  25. 25.

    F. Ahmed, Eur. Phys. J. C 78, 598 (2018). https://doi.org/10.1140/epjc/s10052-018-6082-8

  26. 26.

    L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1971). ISBN 9780750627689

  27. 27.

    A. Papapetrou, Proc. R. Irish Acad. A 52, 11 (1948). http://www.jstor.org/stable/20488488

  28. 28.

    R.C. Tolman, Relativity, Thermodynamics and Cosmology (Oxford University Press, Oxford, 1934). ISBN 978-0486653839

  29. 29.

    P.G. Bergmann, R. Thomson, Phys. Rev. 89, 400 (1953). https://doi.org/10.1103/PhysRev.89.400

  30. 30.

    C. Møller, Ann. Phys. (N.Y.) 4, 347 (1958). https://doi.org/10.1016/0003-4916(58)90053-8

  31. 31.

    C. Møller, Ann. Phys. (N.Y.) 12, 118 (1961). https://doi.org/10.1016/0003-4916(61)90148-8

  32. 32.

    S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972). ISBN 978-0471925675

  33. 33.

    A. Qadir, M. Sharif, Phys. Lett. A 167, 331 (1992). https://doi.org/10.1016/0375-9601(92)90267-P

  34. 34.

    Ö. Yeşiltaş, Eur. Phys. J. Plus 130, 128 (2015). https://doi.org/10.1140/epjp/i2015-15128-y

  35. 35.

    H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, H. Rahimov, Adv. High Energy Phys. 2012, 707041 (2012). https://doi.org/10.1155/2012/707041

  36. 36.

    H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar, Ann. Phys. (Berlin) 525, 944 (2013). https://doi.org/10.1002/andp.201300102

  37. 37.

    L. Fang Deng, C. Yun Long, Z. Wen Long, T. Xu, Adv. High Energy Phys. 2018, 2741694 (2018). https://doi.org/10.1155/2018/2741694

  38. 38.

    F.M. Andrade, E.O. Silva, Eur. Phys. J. C 74, 3187 (2014). https://doi.org/10.1140/epjc/s10052-014-3187-6

  39. 39.

    M. Hosseinpour, H. Hassanabadi, M. de Montigny, Eur. Phys. J. C 79, 311 (2019). https://doi.org/10.1140/epjc/s10052-019-6830-4

  40. 40.

    M. Hosseinpour, F.M. Andrade, E.O. Silva, H. Hassanabadi, Eur. Phys. J. C 77, 270 (2017). https://doi.org/10.1140/epjc/s10052-017-4834-5

  41. 41.

    K. Bakke, Eur. Phys. J. Plus 127, 82 (2012). https://doi.org/10.1140/epjp/i2012-12082-2

  42. 42.

    B.A. Bilby, R. Bullough, E. Smith, Proc. R. Soc. Lond. A 263, 263 (1955). https://www.jstor.org/stable/99752

  43. 43.

    D.V. Gal’tsov, P.S. Letelier, Phys. Rev. D 47, 4273 (1993). https://doi.org/10.1103/PhysRevD.47.4273

  44. 44.

    K. Bakke, F. Moraes, Phys. Lett. A 376, 2838 (2012). https://doi.org/10.1016/j.physleta.2012.09.006

  45. 45.

    K.C. Valanis, V.P. Panoskaltsis, Acta Mech. 175, 77 (2005). https://doi.org/10.1007/s00707-004-0196-9

  46. 46.

    L.H. Ryder, Quantum Field Theory, 2nd edn. (Cambridge University Press, New York, 1996), pp. 436–7

  47. 47.

    P. Collas, D. Klein, The Dirac Equation in Curved Spacetime: A Guide for Calculations (Springer, Berlin, 2019). https://doi.org/10.1007/978-3-030-14825-6

  48. 48.

    A.D. Alhaidari, Ann. Phys. 320, 453 (2005). https://doi.org/10.1016/j.aop.2005.07.001

  49. 49.

    J. Carvalho, C. Furtado, F. Moraes, Phys. Rev. A 84, 032109 (2011). https://doi.org/10.1103/PhysRevA.84.032109

  50. 50.

    L.C.N. Santos, C.C. Barros Jr., Eur. Phys. J. C 76, 560 (2016). https://doi.org/10.1140/epjc/s10052-016-4409-x

  51. 51.

    E.A.F. Braganca, R.L.L. Vitória, H. Belich, E.R. Bezerra de Mello, Relativistic quantum oscillators in the global monopole spacetime (2019). arXiv:1909.00037v1

  52. 52.

    P. Strange, L.H. Ryder, Phys. Lett. A 380, 3465 (2016). https://doi.org/10.1016/j.physleta.2016.08.016

  53. 53.

    M. Nakahara, Geometry, Topology and Physics (Institute of Physics Publishing, Bristol, 1998). ISBN 978-0750306065

  54. 54.

    K. Bakke, H. Mota, Eur. Phys. J. Plus 133, 409 (2018). https://doi.org/10.1140/epjp/i2018-12268-6

  55. 55.

    K. Bakke, C. Furtado, Phys. Rev. D 82, 084025 (2010). https://doi.org/10.1103/PhysRevD.82.084025

  56. 56.

    N.D. Birrel, P.C.W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982). https://doi.org/10.1017/CBO9780511622632

  57. 57.

    W. Greiner, Relativistic Quantum Mechanics: Wave Equations, 3rd edn. (Springer, Berlin, 2000). ISBN: 978-3540674573

  58. 58.

    M. de Montigny, S. Zare, H. Hassanabadi, Gen. Relativ. Grav. 50, 47 (2018). https://doi.org/10.1007/s10714-018-2370-8

  59. 59.

    K. Bakke, Gen. Relativ. Gravit. 45, 1847 (2013). https://doi.org/10.1007/s10714-013-1561-6

  60. 60.

    G.Q. Garcia, J.R. de S. Oliveira, K. Bakke, C. Furtado, Eur. Phys. J. Plus 132, 123 (2017). https://doi.org/10.1140/epjp/i2017-11399-6

  61. 61.

    H.F. Mota, K. Bakke, Gen. Relativ. Gravit. 49, 104 (2017). https://doi.org/10.1007/s10714-017-2266-z

  62. 62.

    P. Schluter, K.H. Wietschorke, W. Greiner, J. Phys. A: Math. Gen. 16, 1999 (1983). https://doi.org/10.1088/0305-4470/16/9/024

  63. 63.

    B.D.B. Figueiredo, I. Damiao Soares, J. Tiomno, Class. Quantum Grav. 9, 1593 (1992). https://doi.org/10.1088/0264-9381/9/6/015

  64. 64.

    P. Sedaghatnia, H. Hassanabadi, F. Ahmed, Eur. Phys. J. C 79, 541 (2019). https://doi.org/10.1140/epjc/s10052-019-7051-6

  65. 65.

    I. C. Yang, I. Radinschi, Chin. J. Phys. 42, 40 (2004). www.ps-taiwan.org/cjp/issues.php

  66. 66.

    M. Sharif, K. Nazir, Braz. J. Phys 38, 156 (2008). https://doi.org/10.1590/S0103-97332008000100028

  67. 67.

    M. Sharif, M. Azam, Int. J. Mod. Phys. A 22, 1935 (2007). https://doi.org/10.1142/S0217751X0703515X

  68. 68.

    F. Ahmed, Ann. Phys. 401, 193 (2019). https://doi.org/10.1016/j.aop.2018.12.005

  69. 69.

    M. Sharif, M. Jamil Amir, Mod. Phys. Lett. A 22, 425 (2007). https://doi.org/10.1142/S0217732307021214. Addendum, Mod. Phys. Lett. A 23 (2008) 3431. https://doi.org/10.1142/S0217732308028156

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Acknowledgements

Marc de Montigny thanks the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support (Grant Number RGPIN-2016-04309).

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Correspondence to Marc de Montigny.

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Zare, S., Hassanabadi, H. & de Montigny, M. Relativistic free fermions in an elastic medium with screw dislocations. Eur. Phys. J. Plus 135, 122 (2020). https://doi.org/10.1140/epjp/s13360-020-00184-3

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