Right sign of spin rotation operator

الأصل · EN

For the fermion transformation in the space all books of quantum mechanics propose to use the unitary operator U n(φ)=(-iφ2(σ· n)), where φ is angle of rotation around the axis n. But this operator turns the spin in inverse direction presenting the rotation to the left. The error of defining of U n(φ) action is caused because the spin supposed as simple vector which is independent from σ-operator a priori. In this work it is shown that each fermion marked by number i has own Pauli-vector σᵢ and both of them change together. If we suppose the global σ-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 n is performed by the operator U+ n(φ)=(+iφ2(σ· n)).