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Fermionic anomalies in quantum-mechanical relativistic problems

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Il Nuovo Cimento B (1971-1996)

Summary

We discuss the existence of ambiguities in the quantization of systems with odd Grassmann degrees of freedom, or anomalies of fermionic nature as we call them, which could lead us to an incorrect quantum counterpart. We propose in this work a way of avoiding such ambiguities in the case of relativistic mechanics, which consists in including the odd degrees of freedom into a generalization of the momentum, that fully contains the anomalies. We consider this generalized momentum as the relevant variable to quantize, mentioning their gauge transformation properties. We illustrate our results with some examples. In particular, we discuss the Dirac oscillator as a typical case of the problems we are dealing with.

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References

  1. Casalbuoni R.,Nuovo Cimento A,33 (1976) 286;35 (1976) 377;Galvao C. A. P. andTeitelboim C.,J. Math, Phys.,21 (1980) 1863;De Alfaro V.,Fubini S. andFurlan G.,Nuovo Cimento A,34 (1976) 569;Fubini S. andRabinovici E.,Nucl Phys. B,245 (1984) 17;Furlan P.,Sotkov G. M. andTodorov I. T.,Riv Nuovo Cimento, Vol.13, no. 2 (1990) and references therein.

    MathSciNet  Google Scholar 

  2. Berezin F. andMarinov M.,Sov. Phys. JETP Lett.,21 (1975) 678;Ann. Phys. (N.Y.),104 (1977) 336;Marinov M.,Sov. Phys. Uspekhi,20 (1977) 179.

    Google Scholar 

  3. Galvao C. A. P. andTeitelboim C.,J. Math. Phys.,21 (1980) 1863.

    Article  MathSciNet  ADS  Google Scholar 

  4. Del Sol A. andMartinez y Romero R. P.,Proceedings of the II International Workshop on Harmonic Oscillators, NASA Conference Publication No. 3286, NASA Scientific and Technical Information Branch, edited byDaesoo Han andK. Bernardo Wolf (1995) p. 327;Pseudoclassical relativistic oscillator, inProceedings of the II International Workshop on Harmonic Oscillators, Cocoyoc, Morelos, Mexico, March 23–25 199b, edited byDaesoo Han andK. B. Wolf,NASA Conference Publication, No. 3286.

  5. Crater H. andVan Alstine P.,Phys. Lett. B,100 (1981) 166;Ann. Phys. (N.Y.),21 (1980) 1863;Ann. Phys. (N.Y.),148 (1983) 57.

    Article  ADS  MATH  Google Scholar 

  6. Galvao C. A. P. andTeitelboim C.,J. Math. Phys.,21 (1980) 1863;Quantization of Gauge Systems, edited byM. Henneaux andC. Teitelboim (Princeton University Press) 1992.

    Article  MathSciNet  ADS  Google Scholar 

  7. Kukulin V. I., Loyola G. andMoshinsky M.,Phys. Lett. A,158 (1991) 19;Centelles M.,Viñas X.,Barranco M. andSchuch P.,Nucl Phys. A,73c (1990) 519.

    Article  MathSciNet  ADS  Google Scholar 

  8. Domíguez-Adame F. andGonzalez M. A.,Europhys. Lett.,13 (1990) 193.

    Article  ADS  Google Scholar 

  9. Moshinsky M. andSzczepaniak A.,J. Phys. A,22 (1989) L817;Moreno M. andZentella A.,J. Phys. A,22 (1989) L821;Moshinsky M.,Loyola G.,Szczepaniak A.,Villegas C. andAquino N.,Proceedings of the Rio de Janerio International Workshop on Relativistic Aspects of Nuclear Physics (World Scientific) 1990;Moshinsky M.,Loyola G. andVillegas C.,J. Math. Phys.,32 (1991) 373.

    Article  MathSciNet  ADS  Google Scholar 

  10. Swamy N. V. V.,Phys. Rev.,180 (1969) 1225;Cook P. A.,Lett. Nuovo Cimento,1 (1971) 419;ItÔ D.,Mori K. andCarreri E.,Nuovo Cimento,51 (1967) 1119;Ginocchio J. N., inSymmetries in Science II, edited byB. Gruber andR. Lenczewski (Plenum Press, New York, N.Y.) 1986.

    Article  MathSciNet  ADS  Google Scholar 

  11. Benítez J., Martinez y Romero R. P. et al., Phys. Rev. Lett.,64 (1990) 1643.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Moreno M. andZentella A.,J. Phys. A,22 (1989) L821.

    Article  MathSciNet  ADS  Google Scholar 

  13. Martinez y Romero R. P. andSalas A. L.,J. Math. Phys.,33 (1992) 1831.

    Article  MathSciNet  ADS  Google Scholar 

  14. Wigner E. P.,Quantum mechanical distribution functions revisited, inPerspectives in Quantum Theory, edited byW. Yourgrau andA. van der Merwe (Dover Publications, New York, N.Y.) 1971.

    Google Scholar 

  15. Castaños O., Frank A., Lopez R. andUrrutia L. F.,Phys. Rev. D,43 (1991) 544.

    Article  ADS  Google Scholar 

  16. Moshinsky M., Loyola G. andSzczepaniak A.,The two body Dirac oscillator, Anniversary Volume in Honor of J. J. Giambiagi, (World Scientific, Singapore) 1990;Moshinsky M.,Loyola G.,Szczepaniak A.,Villegas C. andAquino N., inProceedings of the International Workshop on Relativistic Aspects of Nuclear Physics, edited byT. Kodama et al. (World Scientific, Singapore) 1990.

    Google Scholar 

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Authors and Affiliations

  1. Instituto de Fisica, Universidad Nacional Autónoma de México, Apartado Postal 70-542, 04510, México D.F., México

    A. Del Sol Mesa

  2. Departamento de Fisica, Facultad de Ciencias Universidad National Autónoma de México, Apartado Postal 20-364, 01000, México D.F., México

    R. P. Martínez y Romero

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  1. A. Del Sol Mesa
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  2. R. P. Martínez y Romero
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Mesa, A.D.S., Romero, R.P.M.y. Fermionic anomalies in quantum-mechanical relativistic problems. Nuov Cim B 111, 983–993 (1996). https://doi.org/10.1007/BF02743294

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  • DOI: https://doi.org/10.1007/BF02743294

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