This question comes from section 2.3 of 'Quantum Field Theory' by Lewis Ryder. The discussion is on the Lie Group SU(2). He discusses the transformations of vectors under SU(2). Here it goes:(adsbygoogle = window.adsbygoogle || []).push({});

consider the basic spinor [itex] \xi = \begin{pmatrix} \xi_1 \\ \xi_2 \end{pmatrix} [/itex];

[tex] \xi \to U \xi, [/tex]

[tex]\xi^\dagger \to \xi^\dagger U^\dagger. [/tex]

Then he says, we see that [itex] \xi [/itex] and [itex] \xi^\dagger [/itex] transform in different ways, but we may use the unitarity of [itex] U [/itex] to show that [itex] \begin{pmatrix} \xi_1 \\ \xi_2 \end{pmatrix} [/itex] and [itex] \begin{pmatrix} - \xi_2^* \\ \xi_1^* \end{pmatrix} [/itex] transform in the same way under SU(2).

My question is, what is meant by 'they transform in the same way'? And what is meant by saying that [itex] \xi [/itex] and [itex] \xi^\dagger [/itex] don't transform in the same way?

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# What is meant by two vectors transforming in the same way under SU(2)?

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