i am learning Quaternion now for my EM course. Can someone enlighten me on the correspondence between Quaternion and Pauli Matrix algebra?
The Hamilton multiplication rules differ from the Pauli matrix rules only by a factor of i. It is possible to formulate special relativity with Hamilton quaternions having complex coefficients(called biquaternions) and indeed it was first done that way(Silberstein). It turns out that the formulae of general relativity are simpler with the Pauli quaternions. There is also a very interesting (and possibly significant) relation between the Pauli quaternions and three dimensional Clifford Algebra