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On Quantum Algebra

Published online by Cambridge University Press:  24 October 2008

P. A. M. Dirac
P. A. M. Dirac
Affiliation:
St John's College
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Extract

For the purposes of atomic physics it has been found convenient to introduce the idea of quantities that do not in general satisfy the commutative law of multiplication, but satisfy all the other laws of ordinary algebra. These quantities are called q-numbers, and the numbers of ordinary mathematics c-numbers, while the word number alone is used to denote either a q-number or a c-number. Both q-numbers and c-numbers can occur together in the same piece of analysis, and even in the same equation, as numbers of the two kinds can be added together or multiplied. A c-number may, in fact, be regarded as a special case of the more general q-number. In the particular case when two numbers x; and y satisfy xy = yx, we shall say that x commutes with y. A c-number is assumed to commute with every number.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 4 , October 1926 , pp. 412 - 418
Copyright
Copyright © Cambridge Philosophical Society 1926

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References

* Roy. Soc. Proc. A, vol. 110, p. 561 (1926).CrossRefGoogle Scholar

* Note that a number x that commutes with every number must be a c-number, on account of the axiom that if x is a q-number, there must be a q-number b that makes bxb −1 equal an arbitrary q-number.Google Scholar