Right sign of spin rotation operator

For the fermion transformation in the space all books of quantum mechanics propose to use the unitary operator $widehat{U}_{vec n}(varphi)=exp{(-ifracvarphi2(widehatsigmacdotvec n))}$, 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 $widehatsigma$-operator a priori. In this work it is shown that each fermion marked by number $i$ has own Pauli-vector $widehatsigma_i$ and both of them change together. If we suppose the global $widehatsigma$-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 $widehat{U}^+_{vec n}(varphi)=exp{(+ifracvarphi2(widehatsigmacdotvec n))}$.