- #1

- 85

- 0

## Main Question or Discussion Point

i am learning Quaternion now for my EM course. Can someone enlighten me on the correspondence between Quaternion and Pauli Matrix algebra?

- Thread starter QMrocks
- Start date

- #1

- 85

- 0

i am learning Quaternion now for my EM course. Can someone enlighten me on the correspondence between Quaternion and Pauli Matrix algebra?

- #2

member 11137

metric tensor of the Minkowski's space <=> introduction of the quaternions;

a proposition from Dirac to discuss the Schrödinger equation => introduction of (4-4) matrices built in fine with the (2-2) Pauli's matrices;

Let us call m(a) for a = 0, 1, 2, 3 the different (4-4) matrices; the discussion shows that following relation must hold: m(a). m(b) + m(b). m(a) = 2. g(ab)

where g(ab) is the metric tensor for a Minkowski’s space.

So: not a real good explanation (sorry) but a short exposé of the connections between the actors

- #3

selfAdjoint

Staff Emeritus

Gold Member

Dearly Missed

- 6,786

- 7

From this site: http://home.pcisys.net/~bestwork.1/HamiltonQ/hamilton.htm [Broken]

This quote:

This quote:

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

Last edited by a moderator:

- #4

- 85

- 0

- Last Post

- Replies
- 16

- Views
- 8K

- Last Post

- Replies
- 2

- Views
- 2K

- Replies
- 7

- Views
- 5K

- Replies
- 3

- Views
- 3K

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 15

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 7

- Views
- 2K

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 3

- Views
- 889