# Weyl Vs Majorana

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

Thanks

Homework Helper
welcome to pf!

hi zaybu! welcome to pf! a Weyl spinor (one "n" ) 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] Last edited by a moderator:
LAHLH
aren't Weyl fields two comp spinors? with the Dirac and Majorana fields are four comp being built up from two Weyl fields

Gold Member
A Weyl spinor is one that is purely right or left handed.
A Majorana spinor is one that is its own antiparticle.

Homework Helper
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.

QuantumClue
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:

$$i\dot{\psi_R}=-i \partial_x \psi_R+M \psi_L$$

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

$$i \dot{\psi_L}=+i \partial_x \psi_L+M \psi_R$$

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

$$i\dot{\psi}=-i \alpha \partial_x \psi + M\beta$$

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QuantumClue
Or if you like, Right moving particles are expressed as:

$$\frac{\partial \psi_R}{\partial t}=-\frac{\partial \psi_R}{\partial x}$$

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

Left moving particles are represented by:

$$\frac{\partial \psi_L}{\partial t}=+\frac{\partial \psi_L}{\partial x}$$

QuantumClue
I missed out an imaginary number in the coupled equation. I fixed this early this morning, I am surprised to see it still unfixed.

$$i\dot{\psi}=-i \alpha \partial_x \psi + M\beta$$