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.
Similar content being viewed by others
References
Majorana E.:Nuovo Cimento,14 (1937) 171 (English translation:Sinclair D. A., Tech. Trans. TT-542, National Research Council of Canada).
McLennan J. A.:Phys. Rev.,106 (1957) 821;Case K. M.,Phys. Rev.,107 (1957) 307.
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.
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.
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.
Lee T. D. andYang C. N.:Phys. Rev.,104 (1956) 254;Wu C. S. et al., Phys. Rev.,105 (1957) 1413.
Cabibbo N.,Phys. Rev. Lett.,10 (1963) 531;Kobayashi M. andMaskawa K.,Prog. Theor. Phys.,49 (1975) 652.
Higgs P. W.,Phys. Lett.,12 (1964) 132;Phys. Rev. Lett.,13 (1964) 508;Phys. Rev.,145 (1966) 1156.
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.
Barut A. O.,Electrodynamics and Classical Theory of Fields and Particles (Dover Pub., Inc., New York, N.Y.) 1980.
Berg R. A.,Nuovo Cimento A,42 (1966) 148;Sachs M.,Nuovo Cimento A,43 (1966) 1175.
Novozhikov Yu. V.,Vvedenie v teoriyu elementarnykh chastitz (Nauka, Moscow) 1971 (English translation:Introduction to Elementary Particle Theory (Pergamon Press, Oxford, UK) 1975).
Melosh H. J.,Phys. Rev. D,9 (1974) 1095.
Ahluwalia D. V. andSawicki M. V.,Phys. Rev. D,47 (1993) 5161.
Novozhilov Yu. V. andProkhvatilov E. V.,Teor. Mat. Fiz.,1 (1969) 101 (English translation:Theor. Math. Phys.,1 (1969) 78).
Kondratyuk L. A. andTerent'ev M. V.,Yad. Fiz.,31 (1980) 1087 (English translation:Sov. J. Nucl. Phys.,31 (1980) 561).
Faustov R. N.,Relyativistskie preobrazovaniya odnochastichnykh volnovykh funktsiî, Relativistic transformations of one-particle wave functions, preprint ITF-71-117P, Kiev, Sept. 1971, in Russian.
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.
Dvoeglazov V. V.,Extra Dirac equations, preprint EFUAZ FT-95-13 (hep-th/9504159), Apr. 1995, submitted toNuovo Cimento B.
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.
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.
Dirac P. A. M.,Proc. R. Soc. London, Ser. A,117 (1928) 610;118 (1928) 351.
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.
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).
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.
Brana J. andLjolje K.,Fizika,12 (1980) 217 287.
Belinfante F. J. andPauli W.,Physica,7 (1940) 177.
Barut A. O.,Phys. Rev. Lett.,20 (1968) 893;Physica A,142 (1987) 467, 488.
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.
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.
Nigam B. P. andFoldy L. L.,Phys. Rev.,102 (1956) 1410.
Ahluwalia D. V., Johnson M. B. andGoldman T.,Phys. Lett. B,316 (1993) 102.
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.
Sachs M.,Lett. Nuovo Cimento,32 (1981) 307;Nuovo Cimento,37 (1965) 888;107 (1994) 1709.
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.
Barut A. O.,Phys. Lett. B,73 (1978) 310;Phys. Rev. Lett.,42 (1979) 1251.
Kaplan I. G.,J. Mol. Structure,272 (1992) 187.
Pashkov A. F., private communications (1984–95).
Author information
Authors and Affiliations
Corresponding author
Additional information
The author of this paper has agreed to not receive the proofs for correction.
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02821063