Editing Dirac operator (section)

== History ==

[[W.R. Hamilton]] defined "the square root of the Laplacian" in 1847<ref name="Hamilton1847">{{ cite journal
|author=Hamilton, William Rowan
|title=On quaternions; or on a new system of imaginaries in Algebra
|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
|volume=xxxi
|issue=208
|year=1847
|pages=278–283
|url=
|doi=10.1080/14786444708562643
}}
</ref> in his series of articles about [[quaternion|quaternions]]:
<blockquote>
<...> if we
introduce a new characteristic of operation, <math>\triangleleft</math>, defined with relation to these three symbols
<math>ijk,</math> and to the known operation of partial differentiation, performed with respect to three
independent but real variables <math>xyz,</math> as follows:
<math display="block">
\triangleleft=\frac{i\mathrm{d}}{\mathrm{d}x}+\frac{j\mathrm{d}}{\mathrm{d}y}+\frac{k\mathrm{d}}{\mathrm{d}z};
</math>
''this new characteristic'' <math>\triangleleft</math> ''will have the negative of its symbolic square expressed by the following formula'' :
<math display="block">
-\triangleleft^2=\Big(\frac{\mathrm{d}}{\mathrm{d}x}\Big)^2+\Big(\frac{\mathrm{d}}{\mathrm{d}y}\Big)^2+\Big(\frac{\mathrm{d}}{\mathrm{d}z}\Big)^2;
</math>
of which it is clear that the applications to analytical physics must be extensive in a high degree.
</blockquote>