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13. Bundle Theory of Improper Spin Transformations

Author

Cervantes, D. B., Quiroga, S. L., Perissinotti, L. J., and Socolovsky, M.

Subjects
Quantum Physics, Mathematical Physics
Abstract

{\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 $\hat{T}^2=-1$.}, Comment: 8 pages, Plaintex; titled changed, minor text modifications, one reference completed

Published
2004
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48. OVERWHELMING GENETIC HETEROGENEITY AND EXHAUSTING MOLECULAR DIAGNOSTIC PROCESS IN CHRONIC AND PROGRESSIVE ATAXIAS: FACING IT UP WITH AN ALGORITHM, A GENE, A PANEL AT A TIME

Author

Maturo, J Perez, primary, Zavala, L, additional, Vega, P, additional, González-Morón, D, additional, Medina, N, additional, Salinas, V, additional, Rosales, J, additional, Córdoba, M, additional, Arakaki, T, additional, Garretto, N, additional, Rodríguez-Quiroga, S., additional, and Kauffman, MA, additional

Published
2020
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