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Advances in High Energy Physics
Volume 2016, Article ID 1847620, 7 pages
Research Article

Do Small-Mass Neutrinos Participate in Gauge Transformations?

1Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA
2School of Information Technology, KTH Royal Institute of Technology, 16440 Stockholm, Sweden
3Department of Radiology, New York University, New York, NY 10016, USA

Received 31 March 2016; Revised 25 May 2016; Accepted 12 June 2016

Academic Editor: Theocharis Kosmas

Copyright © 2016 Y. S. Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


Neutrino oscillation experiments presently suggest that neutrinos have a small but finite mass. If neutrinos have mass, there should be a Lorentz frame in which they can be brought to rest. This paper discusses how Wigner’s little groups can be used to distinguish between massive and massless particles. We derive a representation of the group which separates out the two sets of spinors: one set is gauge dependent and the other set is gauge invariant and represents polarized neutrinos. We show that a similar calculation can be done for the Dirac equation. In the large-momentum/zero-mass limit, the Dirac spinors can be separated into large and small components. The large components are gauge invariant, while the small components are not. These small components represent spin- non-zero-mass particles. If we renormalize the large components, these gauge invariant spinors represent the polarization of neutrinos. Massive neutrinos cannot be invariant under gauge transformations.