Re: ??? Quaternions ???---

Zigoteau wrote:

> Just an afterthought. It has just struck me that the need to compute
> rotations in a standard 4D Euclidean space is not thick on the ground.
> However, it might be interesting if you had an algorithm for handling
> Lorentz transformations. Can your quaternion algorithm be extended to
> the case of Lorentz transforms?

I wouldn't have thought quaternions were particularly useful in this case.

As I see it, quaternions are useful for studying rotations in 3 dimensions
because of the covering group

Sp(1) = SU(2) -> SO(3).

The corresponding covering group for Lorentz transformations is

SL(2,C) -> SO(1,3)

which is the basis for spinors,
and I would have thought that was a better analogy.

--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
.

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