Weyl Vs Majorana

  • Thread starter zaybu
  • Start date
  • #1
53
2

Main Question or Discussion Point

Can anyone explain to me what is the difference between a Weyl spinnor and a Majorana spinnor?

Thanks
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
250
welcome to pf!

hi zaybu! welcome to pf! :smile:

a Weyl spinor (one "n" :wink:) is an ordinary 4-component complex-valued spinor representing a spin-1/2 particle like an electron which has an anti-particle

a Majorana spinor is a real-valued spinor representing a spin-1/2 particle which is its own anti-particle

for details, see page 95 ff. (page 102 of the .pdf) of David Tong's "Quantum Field Theory" at http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf" [Broken] :wink:
 
Last edited by a moderator:
  • #3
409
1
aren't Weyl fields two comp spinors? with the Dirac and Majorana fields are four comp being built up from two Weyl fields
 
  • #4
DarMM
Science Advisor
Gold Member
2,370
1,397
A Weyl spinor is one that is purely right or left handed.
A Majorana spinor is one that is its own antiparticle.
 
  • #5
tiny-tim
Science Advisor
Homework Helper
25,832
250
aren't Weyl fields two comp spinors? with the Dirac and Majorana fields are four comp being built up from two Weyl fields
Yes, a 4-component spinor is make up of two 2-component spinors.
 
  • #6
160
0
Can anyone explain to me what is the difference between a Weyl spinnor and a Majorana spinnor?

Thanks
Weyl Spinors are when you have right moving and left moving waves, but are not coupled equations. For instance:

[tex]i\dot{\psi_R}=-i \partial_x \psi_R+M \psi_L[/tex]

described right moving waves. Left movers are described as thus:

[tex]i \dot{\psi_L}=+i \partial_x \psi_L+M \psi_R[/tex]

a Majorana field is a coupled equation, which happens when you introduce a mass term into the Dirac Equation:

[tex]i\dot{\psi}=-i \alpha \partial_x \psi + M\beta[/tex]
 
Last edited:
  • #7
160
0
Or if you like, Right moving particles are expressed as:

[tex]\frac{\partial \psi_R}{\partial t}=-\frac{\partial \psi_R}{\partial x}[/tex]

which represent right moving particles for (ω/k = +1).

Left moving particles are represented by:

[tex]\frac{\partial \psi_L}{\partial t}=+\frac{\partial \psi_L}{\partial x}[/tex]
 
  • #8
160
0
I missed out an imaginary number in the coupled equation. I fixed this early this morning, I am surprised to see it still unfixed.

[tex]i\dot{\psi}=-i \alpha \partial_x \psi + M\beta[/tex]
 

Related Threads on Weyl Vs Majorana

Replies
3
Views
904
  • Last Post
Replies
1
Views
673
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
8
Views
5K
  • Last Post
Replies
8
Views
6K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
2K
Top