I'm currently reading a book on relativistic field theory and I'm trying to understand spinors.(adsbygoogle = window.adsbygoogle || []).push({});

After the author introduces the four parts of the Lorentz group he talks about spinors and group representations:

"....With this concept we see that the 2x2 unimodular matrices A discussed in the previous section form a two-dimensional representation of the restricted Lorentz group L_+ (and arrow up)"

The derivation is not clear to me and the author is very abstract in his explanations. But I want to know how to explicitly derive this unimodular matrices. I know a little bit about group theory, for example how to represent the group Z3 as matrices with this formula [itex][D(g)]_{ij}=<i|D(g)|j>[/itex] and it's simple. I know there is a difference because the Lorentz group is a continuous group but maybe there is also such a simple way to derive the spinor representation. I want to know how to explicitly derive spinors from the Lorentz group.

I know that you can write that a four vector corresponds to a 2x2 matrix via:

[itex]\begin{pmatrix} x^{0}+x^{3} & x^{1}-ix^{2} \\ x^{1}+ix^{2} & x^{0}-x^{3} \end{pmatrix}[/itex]

Now is this already a spinor?

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# Representations of spinors

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