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## Main Question or Discussion Point

I'm currently reading about parity and it's role in QFT and im trying to understand an argument of why parity exchanges right-handed and left-handed spinors. At page 94 in

http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf

David Tong states that

"Under parity, the left and right-handed spinors are exchanged. This follows from the

transformation of the spinors under the Lorentz group. In the chiral representation, we

saw that the rotation and boost transformations for the Weyl spinors u+- are

[tex]u_{\pm} \to e^{i \vec \phi \cdot \vec \sigma/2} u_{\pm}, \ \ u_{\pm} \to e^{ \pm i \vec \chi\cdot \vec \sigma/2} u_{\pm}[/tex]

Under parity, rotations don’t change sign. But boosts do ﬂip sign. This conﬁrms that

parity exchanges right-handed and left-handed spinors

[tex] P: u_{\pm} \to u_{\mp}."[/tex]

I have a few questions to this statement. First of all what does he mean when he say that rotations does not change sign under parity, while boosts does? Any way to see the meaning of this formally (mathematically)?

And how does this confirm that left-handed spinors are changed to right-handed spinors under parity?

http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf

David Tong states that

"Under parity, the left and right-handed spinors are exchanged. This follows from the

transformation of the spinors under the Lorentz group. In the chiral representation, we

saw that the rotation and boost transformations for the Weyl spinors u+- are

[tex]u_{\pm} \to e^{i \vec \phi \cdot \vec \sigma/2} u_{\pm}, \ \ u_{\pm} \to e^{ \pm i \vec \chi\cdot \vec \sigma/2} u_{\pm}[/tex]

Under parity, rotations don’t change sign. But boosts do ﬂip sign. This conﬁrms that

parity exchanges right-handed and left-handed spinors

[tex] P: u_{\pm} \to u_{\mp}."[/tex]

I have a few questions to this statement. First of all what does he mean when he say that rotations does not change sign under parity, while boosts does? Any way to see the meaning of this formally (mathematically)?

And how does this confirm that left-handed spinors are changed to right-handed spinors under parity?