Right sign of spin rotation operator. (arXiv:1801.06129v1 [quant-ph])

For the fermion transformation in the space all books of quantum mechanics
propose to use the unitary operator $\widehat{U}_{\vec
n}(\varphi)=\exp{(-i\frac\varphi2(\widehat\sigma\cdot\vec n))}$, where
$\varphi$ is angle of rotation around the axis $\vec{n}$. But this operator
turns the spin in inverse direction presenting the rotation to the left. The
error of defining of $\widehat{U}_{\vec n}(\varphi)$ action is caused because
the spin supposed as simple vector which is independent from
$\widehat\sigma$-operator a priori. In this work it is shown that each fermion
marked by number $i$ has own Pauli-vector $\widehat\sigma_i$ and both of them
change together. If we suppose the global $\widehat\sigma$-operator and using
the Bloch Sphere approach define for all fermions the common quantization axis
$z$ the spin transformation will be the same: the right hand rotation around
the axis $\vec{n}$ is performed by the operator $\widehat{U}^+_{\vec
n}(\varphi)=\exp{(+i\frac\varphi2(\widehat\sigma\cdot\vec n))}$.

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