Register to reply 
Massive Majorana fermions  nontrivial gauge multiplets? 
Share this thread: 
#1
Jan2214, 01:31 AM

P: 518

From supersymmetry, gauge particles have superpartners, gauginos. Supersymmetry breaking will make all the gauginos massive, since none have been observed. But that has certain problems.
A gauge field is a multiplet in its gauge group where each member corresponds to a generator of that group. That puts the field in the adjoint representation of that group. There's a theorem that states that that rep is always a real rep, so a gauge field can be realvalued instead of complexvalued without loss of generality. A gauge field is a massless vector field in the absence of the Higgs mechanism or anything similar, meaning that it has degrees of freedom corresponding to helicities +1 and 1. By supersymmetry, each gaugefield generator has a corresponding gaugino mode with only two degrees of freedom. That makes gauginos Majorana fields, with helicities +1/2 and 1/2. Is that right about them? If they get mass from SUSY breaking, that would make them massive Majorana fields. Massive Majorana fields follow the Majorana equation  Wikipedia: i*D(ψ) = m*ψ^{c} where ψ is the field, ψ^{c} is its charge conjugate, m is the mass, and D is the derivative operator γ^{μ}.D_{μ} ψ^{c} = i*C.ψ^{*} where C is some matrix, the identity matrix in the Majorana basis. At first sight, it seems as if a massive Majorana field cannot be in a nontrivial rep of a gauge group. But if the rep's groupelement matrices are all real, then it becomes possible. So a Majorana particle can be in any real rep of a gauge group. That includes the adjoint rep, meaning that massive Majorana gauginos are possible. Is that correct? 


Register to reply 
Related Discussions  
Gauge invariance requires gauge bosons, why not for neutral fermions?  Quantum Physics  19  
When will we know whether neutrinos are Majorana fermions?  High Energy, Nuclear, Particle Physics  1  
48 Majorana fermions in type II?  General Physics  0  
Massive Fermions in Four Spatial Dimensions  General Physics  10  
Why gauge bosons, but no gauge fermions  Quantum Physics  47 