How do one describe particles with chirality?

[iamquantized]

1) How do one describe particles with chirality? Dirac and Weyl equation?

2) Are particles of different chirality interacts?

3) Does electron have chirality?

 

[Timo]

1) Weyl spinors describe paricles with a definite chirality. Dirac spinors incorporate degrees of freedom for both chiralities. You can extract the desired chirality from dirac spinors with the projection operator $$P_\pm = 0.5 (1 \pm \gamma^5)$$. As a result, both desciptions are fine and in fact interchangable.

2) Pls try reposting the question.

3) The term "electron" ususally means both, the left-handed and the right-handed electron. You can either treat it as two different Weyl fields (the left- and right-handed electron) or, as usually done, as a single Dirac spinor. In the latter case, you can still unambigiously project on its left- and right-handed components.

 

[iamquantized]

1) Weyl spinors describe paricles with a definite chirality. Dirac spinors incorporate degrees of freedom for both chiralities. You can extract the desired chirality from dirac spinors with the projection operator $$P_\pm = 0.5 (1 \pm \gamma^5)$$. As a result, both desciptions are fine and in fact interchangable.

2) Pls try reposting the question.

3) The term "electron" ususally means both, the left-handed and the right-handed electron. You can either treat it as two different Weyl fields (the left- and right-handed electron) or, as usually done, as a single Dirac spinor. In the latter case, you can still unambigiously project on its left- and right-handed components.

Thank you for the reply.

My difficultly is in trying to visualize what chirality physically means. In solid state system, people usually ascribed electron of one chirality to be electron in the conduction band while the opposite chirality belongs to an unoccupied state (hole) in the valence band. Can I then say the electron is left handed, while the hole is right handed. Electron spins clockwise while hole spins anti-clockwise. Is this correct?

Is there an example that describe how electron with different chirality can interacts? Is the electron hole interaction forming an exciton an example of this?

 

[jtbell]

Please post further responses in the thread in the "Atomic, Solid State, Comp. Physics" forum on the same topic:

https://www.physicsforums.com/showthread.php?t=184812