Talk:Algebra of physical space

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This article was nominated for deletion on January 18 2006. The result of the discussion was keep.

Pauli algebra[edit]

I've added a little to this about the Pauli algebra. I'm stunned to see how little geometric algebra is on Wikipedia. I also added a link back to the article on the Dirac equation through paravectors (which I found confusing, but it's not one of my specialties).

We should have all the various ways of geometrizing quantum mechanics edited in. I can think of the following:

Dirac using paravectors -> done

Dirac and Pauli using through density opertors -> not yet, see Cambridge geometry group for details.

Dirac using Hestenes' method of even subalgebra -> not yet.

Should we have a page labeled "geometrization of quantum mechanics" to list these things? —The preceding unsigned comment was added by CarlBrannen (talk • contribs) 07:38, 26 January 2007 (UTC).[reply]

Paravector[edit]

This article is a follow up of the paravector article, where all the operations are defined. Otherwise it is not understandable.

Complete rewriting[edit]

I am the original creator of this article. The topic is technical so I did not even try to make it self contained. My objective is simply to give a general idea of the topic by showing the most important equations. Cabrer7 00:29, 4 November 2007 (UTC)[reply]

Superfluous markup[edit]

In places there is code like:

L = B R^{\,} for $L=BR^{\,}$
p = m u^{\,}, for $p=mu^{\,},$

Any particular reason? It will be removed in the next few days. Thanks, M∧Ŝc²ħε И_τlk

I'm surprised you ask. It may have been a variant of the now unused PNG forcing approach. Go for it. — Quondum 21:06, 27 August 2013 (UTC)[reply]

The post probably was pointless, but I wasn't sure why there were spaces in superscripts. M∧Ŝc²ħε И_τlk 22:45, 27 August 2013 (UTC)[reply]

Isomorphism[edit]

Is this isomorphic to C ⊗ H? Double sharp (talk) 16:33, 9 April 2016 (UTC)[reply]

Yes. Specifically the even graded elements are isomorphic to real quaternions, the odd graded elements are isomorphic to imaginary quaterions, and the volume element 'pseudoscalar' acts like the commuting imaginary unit of the complex numbers. It's also isomorphic to the algebra of 2x2 complex matrices! JasonHise (talk) 05:36, 7 June 2020 (UTC)[reply]

EM field[edit]

The article includes a section on classical electromagnetism that uses concepts of bivector (complex) and Riemann–Silberstein vector without links or attribution. The so-called "algebra of physical space" lacks acknowledgement of previous work in the field. Rgdboer (talk) 22:57, 30 August 2016 (UTC)[reply]