Little group generators for Dirac neutrino one-particle states

R. Romero


Assuming neutrinos to be of the Dirac type, the little group generators for the one-particle states, created off the vacuum by the field operator, are obtained, both in terms of the one-particle states themselves and in terms of creation/annihilation operators. It is shown that these generators act also as rotation operators in the Hilbert space of the states, providing three types of transformations: a helicity flip, the standard charge conjugation, and a combination of the two, up to phases. The transformations’ properties are provided in detail and their physical implications discussed. It is also shown that one of the transformations continues to hold for chiral fields without mixing them. It is argued that these results provide support for the Majorana nature of massive neutrinos.


Neutrinos; little group; one-particle states; Majorana

Full Text:



Y. Fukuda et al. (Super-Kamiokande), Phys. Rev. Lett.

, 1562 (1998), arXiv:hep-ex/9807003 [hep-ex].

S. Fukuda et al. (Super-Kamiokande), Phys. Rev. Lett.

, 5651 (2001), arXiv:hep-ex/0103032 [hep-ex].

M. H. Ahn et al. (K2K), Phys. Rev. Lett. 90, 041801

(2003), arXiv:hep-ex/0212007 [hep-ex].

Q. R. Ahmad et al. (SNO), Phys. Rev. Lett. 89, 011301

(2002), arXiv:nucl-ex/0204008 [nucl-ex].

K. Eguchi et al. (KamLAND), Phys. Rev. Lett. 90,

(2003), arXiv:hep-ex/0212021 [hep-ex].

T. Araki et al. (KamLAND), Phys. Rev. Lett. 94, 081801

(2005), arXiv:hep-ex/0406035 [hep-ex].

D. G. Michael et al. (MINOS), Phys. Rev. Lett. 97,

(2006), arXiv:hep-ex/0607088 [hep-ex].

M. Zralek, Acta Phys. Polon. B28, 2225 (1997),

arXiv:hep-ph/9711506 [hep-ph].

M. Fukugita and T. Yanagida, Physics of Neutrinos: and

Application to Astrophysics, Theoretical and Mathematical

Physics (Springer Berlin Heidelberg, 2003).

R. N. Mohapatra and P. B. Pal, Massive Neutrinos in

Physics and Astrophysics; 3rd ed., World Scientific Lecture

Notes in Physics (World Scientific, Singapore, 2004).

C. Giunti and C. Kim, Fundamentals of Neutrino Physics

and Astrophysics (OUP, Oxford, 2007).

S. T. Petcov, Adv. High Energy Phys. 2013, 852987

(2013), arXiv:1303.5819 [hep-ph].

L. F. Li and F. Wilczek, Phys. Rev. D25, 143 (1982).

B. Kayser and R. E. Shrock, Physics Letters B 112, 137


B. Kayser, Phys. Rev. D26, 1662 (1982).

S. M. Bilenky and C. Giunti, Int. J. Mod. Phys. A30,

(2015), arXiv:1411.4791 [hep-ph].

I. Ostrovskiy and K. O’Sullivan, Mod. Phys. Lett. A 31,

(2016), [Erratum: Mod. Phys. Lett. A 31, no.23,

(2016)], arXiv:1605.00631 [hep-ex].

S. Dell’Oro, S. Marcocci, M. Viel, and F. Vissani,

Adv. High Energy Phys. 2016, 2162659 (2016),

arXiv:1601.07512 [hep-ph].

J. D. Vergados, H. Ejiri, and F. Simkovic, Int. J. Mod.

Phys. E25, 1630007 (2016), arXiv:1612.02924 [hep-ph].

W. Maneschg, in Prospects in Neutrino Physics (Nu-

Phys2016) London, United Kingdom, December 12-14,

(2017) arXiv:1704.08537 [physics.ins-det].

S. Di, in Prospects in Neutrino Physics (NuPhys2016)

London, United Kingdom, December 12-14, 2016 (2017)

arXiv:1705.03935 [nucl-ex].

M. Hirsch, R. Srivastava, and J. W. Valle, Physics Letters

B 781, 302 (2018), arXiv:1711.06181 [hep-ph].

M. Gell-Mann, P. Ramond, and R. Slansky, in Supergravity

Workshop at Stony Brook, New York, September

-28, 1979, Vol. C790927 (1979) pp. 315–321,

arXiv:1306.4669 [hep-th].

T. Yanagida, in Proceedings of the Workshop on the Unified

Theories and the Baryon Number in the Universe:

Tsukuba, Japan, February 13-14, 1979, Vol. C7902131

(1979) pp. 95–99.

S. L. Glashow, in Quarks and Leptons: Cargèse 1979 ,

edited by M. Lévy, J.-L. Basdevant, D. Speiser, J. Weyers,

R. Gastmans, and M. Jacob (Springer US, Boston,

MA, 1980) pp. 687–713.

R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett.

, 912 (1980).

J. Schechter and J. W. F. Valle, Phys. Rev. D 25, 2951


R. N. Mohapatra and A. Y. Smirnov, Elementary

particle physics. Proceedings, Corfu Summer Institute,

CORFU2005, Corfu, Greece, September 4-26, 2005,

Ann. Rev. Nucl. Part. Sci. 56, 569 (2006), arXiv:hepph/


A. de Gouvêa, Ann. Rev. Nucl. Part. Sci. 66, 197 (2016).

W. Buchmuller, R. D. Peccei, and T. Yanagida,

Ann. Rev. Nucl. Part. Sci. 55, 311 (2005), arXiv:hepph/


P. D. Bari, Contemp. Phys. 53, 315 (2012),

arXiv:1206.3168 [hep-ph].

C. S. Fong, E. Nardi, and A. Riotto, Adv. High Energy

Phys. 2012, 158303 (2012), arXiv:1301.3062 [hep-ph].

E. Wigner, Annals of Mathematics 40, 149 (1939).

W. Tung, Group Theory in Physics (World Scientific,


J. Cornwell, Group Theory in Physics: An Introduction,

Techniques of Physics (Elsevier Science, 1997).

G. Costa and G. Fogli, Lecture Notes in Physics 823, 1


A. Duncan, The Conceptual Framework of Quantum

Field Theory (Oxford University Press, 2012).

M. Peskin and D. Schroeder, An introduction to quantum

field theory, Advanced book program (Addison-Wesley

Pub. Co., 1995).

In this work, the terms left-handed (LH) and righthanded

(RH) always refer to helicity , respectively.

S. Pokorski, Gauge Field Theories, Vol. Cambridge

Monographs on Mathematical Physics (Cambridge University

Press, 2000).

S. F. King, Proceedings, 23rd International Conference

on Neutrino Physics and Astrophysics (Neutrino 2008):

Christchurch, New Zealand, May 26-31, 2008, J. Phys.

Conf. Ser. 136, 022038 (2008), arXiv:0810.0492 [hep-ph].

S. Weinberg, The Quantum Theory of Fields, The Quantum

Theory of Fields 3 Volume Hardback Set No. v. 1

(Cambridge University Press, 1995).



  • There are currently no refbacks.

REVISTA MEXICANA DE FÍSICA, year 67, issue 2, March-April 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946,, e-mail: Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, March 1st., 2021.

The responsibility of the materials published in Revista Mexicana de Física rests solely with their authors and their content does not necessarily reflect the criteria of the Editorial Committee or the Sociedad Mexicana de Física. The total or partial reproduction of the texts hereby published is authorized as long as the complete source and the electronic address of the publications are cited.

There is no fee for article processing, submission or publication.

Revista Mexicana de Física by Sociedad Mexicana de Física, A. C. is distributed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License