Subject: Re: Quaternions

From: Pertti Lounesto
<lounesto@dopey.hut.fi>

Date:
1997/05/02

Message-Id:
<w0ipvvabgdt.fsf@dopey.hut.fi>

Newsgroups:
sci.physics.electromag,sci.physics.relativity

"Srdjan
Budisin" <srdjan@EUnet.yu> writes:

-I would like to
know if complex quaternions are the same as octanions?

No,
octonions are not the same as complex quaternions.

Complex
quaternions are isomorphic to Pauli spin
matrices.

"Srdjan Budisin" <srdjan@EUnet.yu>
writes:

-octanions form an algebra which is not a dividsion
algebra.

No, octonions do form a division algebra.

Also all
non-zero octonions do admit an inverse.

"Srdjan
Budisin" <srdjan@EUnet.yu> writes:

-In this case [of
complex quaternions] we would be living in

-a 6-dimensional
space and a 2-dimensional time.

No, a space-time even would
be represented by sqrt(-1)ct+ix+jy+kz.

"Srdjan
Budisin" <srdjan@EUnet.yu> writes:

-Maybe, Maxwell
equations can be formulated in therms of quatrnions?

-Maybe,
Special Theory of Relativity can be formulated using
Quaternions.

-How about Quantum Mechanics?

Pertti
Lounesto writes:

> No, No, Yes, if you mean real
quaternions.

> Yes, Yes, Yes, for complex quaternions (called
also biquaternions).

I took a look at Doug Sweetser's nice web-
site

http://world.std.com/~sweetser/quaternions/qindex/qindex.
html

and have to re-evaluate my position:

Maxwell equations
can be formulated by real quaternions alone

(but only in Lorentz
gauge, and by a second order diff-equation).

Special theory of
relativity, the Lorentz transformations, can

be formulated by real
quaternions alone (but the Lorentz trans-

formation will depend
also on the point to be transformed).

--

Pertti Lounesto
http://www.math.hut.fi/~lounesto

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