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A spinor has two components that describes its transformation under a lorentz transformation, classified by two indices $\Psi_{a\dot{b}}$, the first transforms under the left part of the lorentz group $SO(1,3)\approx SU(2)_L \otimes SU(2)_R$ (in more detail $\Psi_{a\dot{b}}\rightarrow L(\Lambda)_a^{a'} R(\Lambda)_\dot{b}^{\dot{b}'}\Psi_{a'\dot{b}'}$ where ...

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I'm not very strong in group theory, so could someone please explain in simple terms what it means for the left handed parts to transform as triplets and right handed parts to transform as singlets? How would you go about writing down such terms in a Lagrangian? Groups are abstract. They have elements that can be "multiplied" and they have other ...

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Let's check that parity is violated by the weak interaction lagrangian: $$\mathcal{L}(x) = \bar{\psi}(x) \gamma^\mu \frac{(1-\gamma^5)}{2} \psi(x) W_\mu(x)$$ Saying that parity is violated means that the transformed lagrangian $\mathcal{L}'(x)$ is not equal to the old lagrangian resulting from new coordinates $\mathcal{L}(x')$ where $x'^0 = x^0$ and ...

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