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As i was reading my teacher's notes on SU(2)$SU(2)$ and SO(3)$SO(3)$,i i have had this question. Why do co-spinors transform differently under a rotation than contra-spinors?

As i was reading my teacher's notes on SU(2) and SO(3),i have had this question. Why do co-spinors transform differently under a rotation than contra-spinors?

As i was reading my teacher's notes on $SU(2)$ and $SO(3)$, i have had this question. Why do co-spinors transform differently under a rotation than contra-spinors?

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Co-spinors and contra-spinors

As i was reading my teacher's notes on SU(2) and SO(3),i have had this question. Why do co-spinors transform differently under a rotation than contra-spinors?