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The error is that $\gamma_5$ doesn't intrinsically change sign under parity. Also, don't forget that under parity the spatial components of $W_\mu$ change sign. And also $\gamma^0 \gamma^\mu \gamma^0 \neq \gamma^\mu$.


0

Weak interactions with $W$ and $Z$ gauge bosons violate parity simply because the righ-handed and the left-handed fermions coupled differently to $W$ and $Z$. For example, the $W$'s couple only to the left-handed fields. A parity inviariant dynamics would require that both left- and right- fields couple in the same way to the gauge vector since they get ...


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I guess it is because you first of all change sign of $\vec x$ to $- \vec x$ in physical space(this is parity transformation in a nutshell). All this peculiar algebra concerning left and right chirality fields comes from $J = 1/2$ Lorenz group representation, so transformation rules are defined as representatives of parity transformation of physical space.


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Okay, I think I have an idea why the terminology is used, but I think this argument makes little sense: The Lagrangian term describing weak interactions is of the form $$ \bar \Psi \gamma_\mu P_L \Psi W^\mu $$ Under parity transformations $ \Psi \rightarrow \gamma_0 \Psi$ and $ \bar \Psi \rightarrow \bar \Psi \gamma_0 $, therefore $$ \bar \Psi ...


2

Fermion wavefunctions are antisymmetric under the interchange of two particles. Spatial inversion flips the spatial coordinate, but does not interchange particles. In other words, let's say we have a two particle wave function, $\psi(x_1, x_2)$ (where $x_1$ is the position of particle 1, and $x_2$ is the position of particle 2). Being odd under parity ...


0

well, fermions' "spatial wave function" can also be antisymmetric. I think it's the whole wave function(spin+spatial) that matters.



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