ar X iv : q ua nt - p h / 04 10 07 9 v 1 1 1 O ct 2 00 4 IMPROPER TRANSFORMATIONS OF NON RELATIVISTIC SPIN 12 SPINORS
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چکیده
We first give a geometrical description of the action of the parity operator (ˆ P) on non relativistic spin 1 2 Pauli spinors in terms of bundle theory. The relevant bundle, SU (2) ⊙ Z 2 → O(3), is a non trivial extension of the universal covering group SU (2) → SO(3). ˆ P is the non relativistic limit of the corresponding Dirac matrix operator P = iγ 0 and obeysˆP 2 = −1. Then, from the direct product of O(3) by Z 2 , naturally induced by the structure of the galilean group, we identify, in its double cover, the time reversal operator (ˆ T) acting on spinors, and its product withˆP. Both, ˆ P andˆT , generate the group Z 4 × Z 2. As in the case of parity, ˆ T is the non relativistic limit of the corresponding Dirac matrix operator T = γ 3 γ 1 , and obeysˆT 2 = −1.
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تاریخ انتشار 2004