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I don’t get what this formula is saying... it’s not returning the complex vector that you get from rotating, it’s giving some scalar whose relation to the rotation is not at all clear. Can you elaborate?
It's a 2x2 matrix that acts on a 2 component complex vector (i.e. a spinor).
Wait wait wait, is the dot referring to an outer product and not an inner (dot) product?
IT's referring to an inner product. σ is a vector of pauli matrices.
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Then after "walking in a circle" (i.e. 2π radians), you will actually be upside-down.
