Bundle Theory of Improper Spin Transformations

Details Bundle Theory of Improper Spin Transformations Bundle Theory of Improper Spin Transformations

2004-10-11

arxiv.org/abs/quant-ph/0410079v2

Physics

Quantum Physics

8 pages, Plaintex; titled changed, minor text modifications, one reference completed

Scientific paper

10.1007/s10773-005-2061-6

{\it We first give a geometrical description of the action of the parity operator ($\hat{P}$) on non relativistic spin ${{1}\over{2}}$ Pauli spinors in terms of bundle theory. The relevant bundle, $SU(2)\odot \Z_2\to O(3)$, is a non trivial extension of the universal covering group $SU(2)\to SO(3)$. $\hat{P}$ is the non relativistic limit of the corresponding Dirac matrix operator ${\cal P}=i\gamma_0$ and obeys $\hat{P}^2=-1$. 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 ($\hat{T}$) acting on spinors, and its product with $\hat{P}$. Both, $\hat{P}$ and $\hat{T}$, generate the group $\Z_4 \times \Z_2$. As in the case of parity, $\hat{T}$ is the non relativistic limit of the corresponding Dirac matrix operator ${\cal T}=\gamma^3 \gamma^1$, and obeys $\hat{T}^2=-1$.}

Affiliated with

Also associated with

No associations

Rating

Bundle Theory of Improper Spin Transformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bundle Theory of Improper Spin Transformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bundle Theory of Improper Spin Transformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-714776