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- Thread starter zaybu
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tiny-tim

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hi zaybu! welcome to pf!

a Weyl spinor (

a Majorana spinor is a

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]

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DarMM

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A Majorana spinor is one that is its own antiparticle.

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tiny-tim

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Yes, a 4-component spinor is make up of two 2-component spinors.

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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]

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[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]

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

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