Skip to main content
Log in

Lagrangian for the Majorana-Ahluwalia construct

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

Equations describing self/anti-self-charge conjugate states, recently proposed by Ahluwalia, are re-written in covariant form. The corresponding Lagrangian for the neutral-particle theory is proposed. From a group-theoretical viewpoint the construct is an example of the Nigam-Foldy-Bargmann-Wightman-Wigner-type quantum field theory based on the doubled representations of the extended Lorentz group. Relations with the Sachs-Schwebel and Ziino-Barut concepts of relativistic quantum theory are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Majorana E.:Nuovo Cimento,14 (1937) 171 (English translation:Sinclair D. A., Tech. Trans. TT-542, National Research Council of Canada).

    Article  Google Scholar 

  2. McLennan J. A.:Phys. Rev.,106 (1957) 821;Case K. M.,Phys. Rev.,107 (1957) 307.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Ahluwalia D. V., Johnson M. B. andGoldman T. Mod. Phys. Lett. A,9 (1994) 439;Acta Phys. Polon. B,25 (1994) 1267;Ahluwalia D. V.,Incompatibility of self-charge conjugation with helicity eigenstates and gauge interactions, preprint LA-UR-94-1252 (hep-th/9404100), Los Alamos, Apr. 1994;McLennan-case construct for neutrino, its generalization, and a fundamentally new wave equation, preprint LA-UR-94-3118 (hep-th/9409134), Los Alamos, Sept. 1994, to be published inInt. J. Mod. Phys. A.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Athanassopoulos C. et al., Candidate events in a search for \(\bar \nu _\mu \to \bar \nu _e \) oscillations, preprint LANL LA-UR-95-1238 (nucl-ex/9504002), Los Alamos, Apr. 1995, submitted toPhys. Rev. Lett.

  5. Glashow S. L.,Nucl. Phys.,22 (1961) 579;Weinberg S.,Phys. Rev. Lett.,19 (1967) 1264;Salam A. inProceedings of the VIII Nobel Symposium, Stockholm, 1968, edited byN. Svartholm, p. 367.

    Article  Google Scholar 

  6. Lee T. D. andYang C. N.:Phys. Rev.,104 (1956) 254;Wu C. S. et al., Phys. Rev.,105 (1957) 1413.

    Article  ADS  Google Scholar 

  7. Cabibbo N.,Phys. Rev. Lett.,10 (1963) 531;Kobayashi M. andMaskawa K.,Prog. Theor. Phys.,49 (1975) 652.

    Article  ADS  Google Scholar 

  8. Higgs P. W.,Phys. Lett.,12 (1964) 132;Phys. Rev. Lett.,13 (1964) 508;Phys. Rev.,145 (1966) 1156.

    Article  ADS  Google Scholar 

  9. For recent review see:Gelmini G. andRoulet E.,Neutrino masses, preprint UCLA/94/TEP/36 (hep-ph/9412278), Nov. 1994, to be published inRep. Prog. Phys.

  10. Barut A. O.,Electrodynamics and Classical Theory of Fields and Particles (Dover Pub., Inc., New York, N.Y.) 1980.

    Google Scholar 

  11. Berg R. A.,Nuovo Cimento A,42 (1966) 148;Sachs M.,Nuovo Cimento A,43 (1966) 1175.

    Article  ADS  Google Scholar 

  12. Novozhikov Yu. V.,Vvedenie v teoriyu elementarnykh chastitz (Nauka, Moscow) 1971 (English translation:Introduction to Elementary Particle Theory (Pergamon Press, Oxford, UK) 1975).

    Google Scholar 

  13. Melosh H. J.,Phys. Rev. D,9 (1974) 1095.

    Article  ADS  Google Scholar 

  14. Ahluwalia D. V. andSawicki M. V.,Phys. Rev. D,47 (1993) 5161.

    Article  ADS  Google Scholar 

  15. Novozhilov Yu. V. andProkhvatilov E. V.,Teor. Mat. Fiz.,1 (1969) 101 (English translation:Theor. Math. Phys.,1 (1969) 78).

    Article  Google Scholar 

  16. Kondratyuk L. A. andTerent'ev M. V.,Yad. Fiz.,31 (1980) 1087 (English translation:Sov. J. Nucl. Phys.,31 (1980) 561).

    MathSciNet  Google Scholar 

  17. Faustov R. N.,Relyativistskie preobrazovaniya odnochastichnykh volnovykh funktsiî, Relativistic transformations of one-particle wave functions, preprint ITF-71-117P, Kiev, Sept. 1971, in Russian.

  18. Dvoeglazov V. V.,Significance of the spinorial basis in relativistic quantum mechanics, preprint EFUAZ FT-95-12 (hep-th/9504134), Mar. 1995, submitted toNuovo Cimento B.

  19. Dvoeglazov V. V.,Extra Dirac equations, preprint EFUAZ FT-95-13 (hep-th/9504159), Apr. 1995, submitted toNuovo Cimento B.

  20. Dvoeglazov, V. V.,Neutral particles in light of the Majorana-Ahluwalia ideas, preprint EFUAZ FT-95-11 (hep-th/9504158), Feb. 1995, to be published inInt. J. Theor. Phys.

  21. Ziino G.,Ann. Fond. L. de Broglie,14 (1989) 427;16 (1991) 343;Barut A. O. andZiino G.,Mod. Phys. Lett. A,8 (1993) 1011.

    Google Scholar 

  22. Dirac P. A. M.,Proc. R. Soc. London, Ser. A,117 (1928) 610;118 (1928) 351.

    Article  ADS  MATH  Google Scholar 

  23. Weinberg S.,Phys. Rev. B,133 (1964) 1318;134 (1964) 882;181 (1969) 1893;Phys. Lett.,9. (1964) 357;Phys. Rev. B,135 (1964) 1049;138 (1965) 988.

    Article  MathSciNet  ADS  Google Scholar 

  24. Gelfand I. M. andTsetlin M. L.,Ž. Ėksp. Teor. Fiz.,31 (1956) 1107 (English translation:Sov. Phys. JETP,4 (1957) 947);Sokolik G. A.,Ž. Ėksp. Teor. Fiz.,33 (1957) 1515 (English translation:Sov. Phys. JETP,6 (1958) 1170).

    Google Scholar 

  25. Markov M. A.,Ž. Ėksp. Teor. Fiz.,7 (1937) 579, 603;On the difference between muon and electron masses (On two types of Dirac fields), preprint JINR D-1345, Dubna, 1963.

    Google Scholar 

  26. Brana J. andLjolje K.,Fizika,12 (1980) 217 287.

    Google Scholar 

  27. Belinfante F. J. andPauli W.,Physica,7 (1940) 177.

    Article  MathSciNet  ADS  Google Scholar 

  28. Barut A. O.,Phys. Rev. Lett.,20 (1968) 893;Physica A,142 (1987) 467, 488.

    Article  ADS  Google Scholar 

  29. Wigner E. P., inGroup theoretical Concepts and Methods in Elementary Particle Physics, Lectures of the Istanbul Summer School of Theoretical Physics, 1962, edited byF. Gürsey.

  30. Dirac P. A. M., inMathematical Foundations of Quantum Theory (Academic Press, Inc.) 1978, p. 1;Proc. Cambridge Philos. Soc.,30 (1934) 150;Proc. R. Soc. London, Ser. A,322 (1971) 435;328 (1972) 1.

  31. Nigam B. P. andFoldy L. L.,Phys. Rev.,102 (1956) 1410.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Ahluwalia D. V., Johnson M. B. andGoldman T.,Phys. Lett. B,316 (1993) 102.

    Article  MathSciNet  ADS  Google Scholar 

  33. Sachs M.,Ann. Phys.,6 (1959) 244;Nuovo Cimento Suppl.,21, X (1961) 197;J. Math. Phys.,3 (1962) 843;Nuovo Cimento,34 (1964) 81;Found. Phys.,10 (1980) 921;11 (1981) 329.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Sachs M.,Lett. Nuovo Cimento,32 (1981) 307;Nuovo Cimento,37 (1965) 888;107 (1994) 1709.

    Article  ADS  Google Scholar 

  35. Bilenky S. M. et al., Neutrino oscillations in the framework of three-generation mixing with mass hierarchy, preprint DFTT 25/95, JHU-TIPAC 95013 (hep-ph/9504405), Apr. 1995.

  36. Barut A. O.,Phys. Lett. B,73 (1978) 310;Phys. Rev. Lett.,42 (1979) 1251.

    Article  MathSciNet  ADS  Google Scholar 

  37. Kaplan I. G.,J. Mol. Structure,272 (1992) 187.

    Article  ADS  Google Scholar 

  38. Pashkov A. F., private communications (1984–95).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. V. Dvoeglazov.

Additional information

The author of this paper has agreed to not receive the proofs for correction.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dvoeglazov, V.V. Lagrangian for the Majorana-Ahluwalia construct. Nuov Cim A 108, 1467–1476 (1995). https://doi.org/10.1007/BF02821063

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02821063

PACS 11.10.Ef

PACS 11.30.Cp

Navigation