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1

In such cases it is very helpful to write a and b in such a way that your first equation is automatically satisfied and the overall phase is neglected. I would take: $$\Psi = (\cos\theta,e^{i\phi}\sin\theta)^T$$ You only have to find 2 free parameters now. Concerning your edit. $\theta$ (your definition) is either 0 or $\pi$, which leaves the two ...

3

Eq. (4.4.11g) is for a Majorana spinor SUSY charges $Q_a$, $a=1,2,3,4$, while eq. (3.1.31) is for left Weyl spinor SUSY charges $Q_{\alpha}$, $\alpha=1,2$.

8

Transformations of the Faraday tensor by the spinor map and Lorentz transformation calculations are often less messy than their $S0(1,\,3)$ counterparts. Even the most everyday and mundane EM calculations (without needing to do Lorentz transformations) can benefit from this: I have in my time written many lines of code to simulate electromagnetic ...

1

I cannot be sure, but I suspect that you can get analytical solutions of the Pauli equation by taking a non-relativistic limit of analytical solutions of the Dirac equation. The latter can be found in many books, say Bagrov, Vladislav G. / Gitman, Dmitry, The Dirac Equation and its Solutions (http://www.degruyter.com/view/product/177851) (you can find a ...

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