Spinor Pauli

The wavefunctions representing the eigenstates of the electron s spin are then two-component vectors (Pauli spinors)... 

So the ring of the iOk Pauli matrices and the set without any proper structure of the Pauli spinors may be unified in a single real field, the only field one can associate with a real space Rn for n > 2. 

Note. In what follows, the identification of the Hamilton quaternion q and the Hestenes spinor tjj with the Pauli spinor and the Dirac spinor P is based on the articles [28,44]. Perhaps, it is not the shortest one, but it allows a step-by-step conversion of P into vice versa when P is expressed by means of its four complex components. 

Teichteil et al developed the angular part (spherical harmonic spinors) of the Pauli spinors as functions of the spatial spherical harmonics [43] ... 

Hence, the sign in the subscript of only affects the eigenvalue of the equation for l. For later convenience in chapter 6, we investigate the Pauli spinors of Eqs. (4.161) and (4.163) further (cf. chapter 6). In particular, the operator cr r)/r = (cr r) will become important. This is a scalar operator, which therefore does not change the total angular momentum. This (2 x 2)-matrix... 

In order to elucidate whether (tr f) leaves the spherical spinor unchanged or whether it switches from the (+) to the (—) spinor of the pair (or vice versa), we study the parity properties of the spherical spinors. By operating with the parity operator P on the Pauli spinors we find... 

The orthonormality of the spherical harmonics and of the spin eigenvectors psnts (with s = 1/2 and OTs = 1/2) ensures orthonormality of the Pauli spinors,... 

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