William Rowan Hamilton shows that the square root of the ordinary three-dimensional Laplacian can be obtained through the use of quaternions: (id/dx + jd/dy + kd/dz)^2 = -(d/dx)^2 -(d/dy)^2 -(d/dz)^2 = -nabla^2; this result will be fundamental to deriving the wave operator (or d’Alambertian) and the Dirac operator of the Klein-Gordon equation of Quantum Field Theory (quantum theory + special relativity).
