Majorana mass term for the electron

  • #1
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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
 
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  • #2
Please write down the Majorana mass term, and identify its elements - e.g. this is a left-handed electron field.
 
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  • #3
Alternatively, just check how such a term would behave under a U(1)_EM transformation. You should find it is not invariant
 
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  • #4
Vanadium 50 said:
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
 
  • #5
zaman786 said:
and left handed electron field comes in doublet
Well, it does, but you still haven't written down what I asked.
 
  • #6
Vanadium 50 said:
Well, it does, but you still haven't written down what I asked.
Majorana=1/2mψˉcψ
 
  • #7
zaman786 said:
Majorana=1/2mψˉcψ
1707939515123.png
 
  • #8
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?
 
  • #9
1708056164359.png

sorry , for delay
 
  • #10
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.
 
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  • #11
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:

zaman786 said:
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?”
 
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  • #12
kindly see my working - in attached file
 

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  • majorana mass term for electron.pdf
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  • #13
actually , i am struggling in this field - and i am in isolation - but trying to proceed -
 

Attachments

  • majorana mass term for electron.pdf
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  • #14
Vanadium 50 said:
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.
 

Attachments

  • majorana mass term for electron.pdf
    503.9 KB · Views: 4
  • #15
i am trying - but thanks for your reply
 
  • #16
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/
 
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  • #17
th
Vanadium 50 said:
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 -
 

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