Spinor Representation of Finite Rotations of SO(4)

Authors

  • Muneer Ahmad Rashid (Rtd) Department of Mathematics National University of Science and Technology (NUST), Islamabad.
  • Ansaruddin Syed Department of Mathematics Jinnah University for Women, Karachi.

Keywords:

Rotation group SO(4), Unitary group SU(2), Spinors, Homomorphism

Abstract

Following the work of C. B. van Wyk on the Lorentz group SO(3, 1), we first express a general finite rotation of SO(4) in terms of 2 ordinary (3-dimensional) vectors a and b satisfying certain conditions and then using the homomorphism of SU(2) × SU(2) onto SO(4), we express the same rotation in terms of a pair of 2 × 2 matrices, again determined by the same pair of vectors a and b. This is extremely useful as it allows one to convert the 4 × 4 matrix multiplication of elements of SO(4) into the 2 × 2 matrix multiplication of elements of SU(2).

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Published

2017-04-30

Issue

Vol. 49 No. 1 (2017)

Section

Articles

License

Copyright (c) 2017 Muneer Ahmad Rashid (Rtd), Ansaruddin Syed

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Spinor Representation of Finite Rotations of SO(4). (2017). Punjab University Journal of Mathematics, 49(1), 98-119. https://pujm.pu.edu.pk/index.php/pujm/article/view/87