Difference between Weyl and Majorana spinors

[zaybu]

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

Thanks

 

[tiny-tim]

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"

 

[LAHLH]

aren't Weyl fields two comp spinors? with the Dirac and Majorana fields are four comp being built up from two Weyl fields

 

[DarMM]

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

 

[tiny-tim]

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:

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

 

[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.

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