scholarly journals Loop Representation of Wigner’s Little Groups

Symmetry ◽  
2017 ◽  
Vol 9 (7) ◽  
pp. 97 ◽  
Author(s):  
Sibel Başkal ◽  
Young Kim ◽  
Marilyn Noz
Keyword(s):  
Wigner’S Little Groups

scholarly journals Do Small-Mass Neutrinos Participate in Gauge Transformations?

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Y. S. Kim ◽  
G. Q. Maguire ◽  
M. E. Noz
Keyword(s):  
Small Mass ◽  
Large Momentum ◽  
Mass Limit ◽  
Finite Mass ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Zero Mass ◽  
Massive Neutrinos ◽  
Wigner’S Little Groups ◽  
Dirac Spinors

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 theSL(2,c)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-1/2non-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.

scholarly journals HOPF MAPS AND WIGNER'S LITTLE GROUPS

2011 ◽  
Vol 26 (19) ◽  
pp. 1393-1405 ◽  
Author(s):  
RUBEN MKRTCHYAN ◽  
ARMEN NERSESSIAN ◽  
VAHAGN YEGHIKYAN
Keyword(s):  
Explicit Formulas ◽  
The Third ◽  
Hopf Fibrations ◽  
Simple Action ◽  
Wigner’S Little Groups ◽  
Simplified Form

We present the explicit formulas relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one. Corresponding invariant Lagrangians are presented, and their possible reductions are discussed.

Sign in / Sign up

Export Citation Format

Share Document