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Anticommuting Linear Transformations

Published online by Cambridge University Press:  20 November 2018

H. Kestelman
H. Kestelman*
Affiliation:
University College, London
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It is well known that any set of four anticommuting involutions (see §2) in a four-dimensional vector space can be represented by the Dirac matrices

(1)

where the B1,r are the Pauli matrices

(2)

(See (1) for a general exposition with applications to Quantum Mechanics.) One formulation, which we shall call the Dirac-Pauli theorem (2; 3; 1), is

Theorem 1. If M1,M2, M3, M4 are 4 X 4 matrices satisfying

then there is a matrix T such that

and T is unique apart from an arbitrary numerical multiplier.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 614 - 624
Copyright
Copyright © Canadian Mathematical Society 1961

References

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