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Forming groups with 4 × 4 matrices

Published online by Cambridge University Press:  23 January 2015

J. R. Harris
J. R. Harris*
Affiliation:
6 Willowdene Court, Bembridge PO35 5SS
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Extract

The three Pauli matrices are normally given [1] as the 2 × 2 matrices:

where ‘i’ is the usual complex number imaginary unit.

These matrices obey the relations a2 = I = b2 = c2(where I is the 2 × 2 identity matrix), as well as the anticommutation relations:

Within the quantities ia,ib and ic,i is a scalar multiplier of the 2 × 2 Pauli matrices and, of course, commutes with each of a, b, c.

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 531 , November 2010 , pp. 426 - 429
Copyright
Copyright © The Mathematical Association 2010

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References

1. Maxwell, E. A., Algebraic structure and matrices, Cambridge University Press (1965) p. 192.Google Scholar
2. Copson, E. T., Theory of functions of a complex variable, Oxford University Press (1935) pp. 1–5.Google Scholar
3. Sawyer, W. W., A path to modern mathematics, Penguin (1966) p. 142.Google Scholar
4. Ledermann, W., Introduction to the theory of finite groups (4th edn.), Oliver & Boyd (1961).Google Scholar