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Does anyone know if the notion of a Dirac measure was named after P.A.M. Dirac? If yes, did he actually introduce it, or is it because integration w.r.t. a Dirac measure does what the so-called Dirac delta function is supposed to be used for?

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    $\begingroup$ yes of course. it is very likely however that he didn't know any measure theory at all, and distribution theory neither (in fact it was developed by schwartz in the 1950's). $\endgroup$ – user55315 Jan 29 '13 at 17:12
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Yes, the Dirac measure is so named because it performs the same action as Dirac's "delta function." I don't believe Dirac used the measure theory formalism, however - he was a physicist.

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I believe Dirac Measure, Dirac distribution, and Dirac function (an entrenched misnomer) are synonyms for the "unit impulse". The unit impulse was used before P. A. M. Dirac by Cauchy, Poisson, Kirchhoff, and Helmholtz but they did not call it the Dirac measure, distribution, or function. Dirac called it the Delta function in his quantum theory work and the name stuck. So It was named after Dirac--the Dirac Delta Function.

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    $\begingroup$ Did Dirac really call it the Dirac function? It's very unusual for people to name things after themselves, especially when they already existed. Do you have a reference to support this? $\endgroup$ – Nate Eldredge May 4 '14 at 15:33
  • $\begingroup$ The Dirac delta function as such was introduced as a "convenient notation" by Paul Dirac in his influential 1930 book Principles of Quantum Mechanics.[17] He called it the "delta function" since he used it as a continuous analogue of the discrete Kronecker delta. $\endgroup$ – user45664 May 4 '14 at 22:23
  • $\begingroup$ Sorry, he called it the Delta Function. Others called it the Dirac Delta Function. $\endgroup$ – user45664 May 4 '14 at 22:24

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