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Quaternionic Aharonov–Bohm Effect

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Abstract

A quaternionic analog of the Aharonov–Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics. A quaternionic phase links the solutions obtained to ordinary complex wave functions, and new theoretical studies and experimental tests are possible for them.

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References

  1. Adler, S.L.: Does the Peres experiment using photons test for hyper-complex (quaternionic) quantum theories? (2016) arXiv:1604.04950 [quant-ph]

  2. Adler, S.L.: Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, Oxford (1995)

    MATH  Google Scholar 

  3. Atiyah, M.F.: Geometry of Yang-Mills fields. Publications of the Scuola Normale Superiore, Pisa (1979)

    MATH  Google Scholar 

  4. Brumby, S.P., Joshi, G.C.: Experimental status of quaternionic quantum mechanics. Chaos Solitons Fractals 7, 747–752 (1996). arXiv:quant-ph/9610009

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Davies, A.J.: Quaternionic Dirac equation. Phys. Rev. D 41, 2628–2630 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  6. Davies, A.J., McKellar, B.H.J.: Nonrelativistic quaternionic quantum mechanics in one dimension. Phys. Rev. A 40, 4209–4214 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  7. Davies, A.J., McKellar, B.H.J.: Observability of quaternionic quantum mechanics. Phys. Rev. A 46, 3671–3675 (1989)

    Article  ADS  Google Scholar 

  8. De Leo, S., Ducati, G., Giardino, S.: Quaternioninc Dirac Scattering. J. Phys. Math. 6:1000130 (2015) arXiv:1505.01807 [math-ph]

  9. De Leo, S., Giardino, S.: Dirac solutions for quaternionic potentials. J. Math. Phys., 55:022301–10 (2014) arXiv: 1311.6673 [math-ph]

  10. De Leo, S., Ducati, G.: Quaternionic differential operators. J. Math. Phys. 42, 2236–2265 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. De Leo, S., Ducati, G.: Quaternionic potentials in non-relativistic quantum mechanics. J. Phys. A35, 5411–5426 (2002)

    ADS  MathSciNet  MATH  Google Scholar 

  12. De Leo, S., Ducati, G.: Quaternionic bound states. J. Phys. A35, 3443–3454 (2005)

    MathSciNet  MATH  Google Scholar 

  13. De Leo, S., Ducati, G.: Quaternionic wave packets. J. Math. Phys. 48, 052111 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. De Leo, S., Rotelli, P.: The Quaternion scalar field. Phys. Rev. D 45, 575–579 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  15. Devchand, C., Ogievetsky, V.: Four-dimensional integrable theories. Lect. Notes Phys. 447, 169 (1995). arXiv:hep-th/9410147

    Article  ADS  MathSciNet  Google Scholar 

  16. Evans, M., Gursey, F., Ogievetsky, V.: From 2-D conformal to 4-D selfdual theories: quaternionic analyticity. Phys. Rev. D 47, 3496–3508 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  17. Giardino, S.: Quaternionic particle in a relativistic box. Found. Phys. 46(4):473–483 (2016) arXiv:1504.00643 [quant-ph]

  18. Maia, M.D., Bezerra, V.B.: Geometric phase in quaternionic quantum mechanics. Int. J. Theor. Phys. 40, 1283–1294 (2001). arXiv:hep-th/0107107

    Article  MathSciNet  MATH  Google Scholar 

  19. Procopio, L.M., Rozema, L.A., Dakić, B., Walther, P.: Comment on Adler’s. Does the Peres experiment using photons test for hyper-complex (quaternionic) quantum theories?. arXiv:1607.01648 [quant-ph] (2016)

  20. Procopio, L.M., Rozema, L.A., Wong Z.J., Hamel, D.R., O’Brien, K., Zhang, X., Dakic, B., Walther P.: Experimental Test of Hyper-Complex Quantum Theories. (2016) arXiv:1602.01624 [quant-ph]

  21. Vaz, J., da Rocha, R.: An Introduction to Clifford Algebras and Spinors. Oxford University Press, Oxford (2016)

    Book  MATH  Google Scholar 

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Correspondence to Sergio Giardino.

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Communicated by Jayme Vaz

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Giardino, S. Quaternionic Aharonov–Bohm Effect. Adv. Appl. Clifford Algebras 27, 2445–2456 (2017). https://doi.org/10.1007/s00006-017-0766-2

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  • DOI: https://doi.org/10.1007/s00006-017-0766-2

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