A Majorana mass term for the electron

[zaman786]

TL;DR Summary

violation of charge conservation of Majorana mass term

hi, while studying Majorana mass term can be added for the neutrino - as they are neutral - but cannot be added for the electron -as it would violate the charge conservation - i could not understand how charge conservation for Majorana mass term of electron is violated.
kindly help

 

[Vanadium 50]

Please write down the Majorana mass term, and identify its elements - e.g. this is a left-handed electron field.

 

[Orodruin]

Alternatively, just check how such a term would behave under a U(1)_EM transformation. You should find it is not invariant

 

[zaman786]

Please write down the Majorana mass term, and identify its elements - e.g. this is a left-handed electron field.

and left handed electron field comes in doublet

 

[Vanadium 50]

and left handed electron field comes in doublet

Well, it does, but you still haven't written down what I asked.

 

[zaman786]

Well, it does, but you still haven't written down what I asked.

Majorana=1/2mψˉcψ

 

[zaman786]

Majorana=1/2mψˉcψ

 

[Vanadium 50]

Well, after almost a week, we are almost halfway there.

Please write down the Majorana mass term, and identify its elements - e.g. this is a left-handed electron field.

Further, what you wrote down is NOT what the images shows.

If you're not willing to put in any work, why should I?

 

[zaman786]

sorry , for delay

 

[Vanadium 50]

Enough is enough. I keep asking you to please write down the Majorana mass term, and identify its elements - e.g. this is a left-handed electron field. and you keep not doing it.

Maybe someone else will help you. I am concluding this is a waste of time. If it's not worth your time to write down the next step of the problem. it can't be worth my time to help you with the step after that.

 

[Orodruin]

I think they believe they have done what you ask. It would seem to be a problem of ability rather than refusal. But maybe that’s just my reading.

The really simple thing to do though is to look at the terms here:

View attachment 340396
sorry , for delay

and do a U(1)_EM transformation. Since the electron is charged under EM, this will mean $\psi_{eL} \to e^{i\phi} \psi_{eL}$ for some $\phi$. Then the OP should be able to answer the question ”is the Majorana mass term invariant?”

 

[zaman786]

kindly see my working - in attached file

 

[zaman786]

actually , i am struggling in this field - and i am in isolation - but trying to proceed -

 

[zaman786]

Enough is enough. I keep asking you to please write down the Majorana mass term, and identify its elements - e.g. this is a left-handed electron field. and you keep not doing it.

Maybe someone else will help you. I am concluding this is a waste of time. If it's not worth your time to write down the next step of the problem. it can't be worth my time to help you with the step after that.

 

[zaman786]

i am trying - but thanks for your reply

 

[Vanadium 50]

I don't think you understand what any of the terms mean - that's why you can't answer my hint.question, and that's why you still have questions after a perfectly good answer has been posted twice. You need to back up a few chapters and learn what the terms you are writing down mean.

You might also want to tale the time to learn to post equations here. PDFs of scribblings are not helpful/

 

[zaman786]

th

I don't think you understand what any of the terms mean - that's why you can't answer my hint.question, and that's why you still have questions after a perfectly good answer has been posted twice. You need to back up a few chapters and learn what the terms you are writing down mean.

You might also want to tale the time to learn to post equations here. PDFs of scribblings are not helpful/

thanks for your guidance- i have books on particle - but i will appreciate if you recommend some -