Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: geometric algebra

Bottom of Page

1 to 12 of 12

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 15th 2016

    gave geometric algebra an Idea-section

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 15th 2016

    That prompted a trip back to your discussion of geometric algebra, including lengthy extracts from Clifford algebra and the interpretation of quantum mechanics (pdf) and the claim

    the electron is a quaternion

    Further back you were helping us visualise the superstring.

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeDec 15th 2016

    Remember that Geometric Algebra was also the title of a lovely book by Emil Artin. It introduces Clifford algebras around page 190

    • CommentRowNumber4.
    • CommentAuthorDexter Chua
    • CommentTimeDec 22nd 2016

    It appears that there is also a page Geometric Algebra with very similar content.

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeDec 23rd 2016

    @Dexter: In principle, a page with that title ought to be about Artin's book.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2016

    Thanks. I have fixed it now. Added disambiguation lines and made “Geometric Algebra” a stub for a category:reference page.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 16th 2019
    • (edited May 16th 2019)

    added pointer to

    • Chis Doran, Geometric Algebra and its Application to Mathematical Physics, 1994 (pdf)

    diff, v3, current

  8. Scalars in geometric algebra are real numbers making geometric algebra the real Clifford algebra.

    Anonymous

    diff, v4, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2020

    I have reverted and adjusted my original wording by mentioning real numbers as a ground field. (We really can’t claim that “geometric algebra is s subfield of Clifford algebra. It’s just playing with Clifford algebra in an ideosyncratic way.)

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 1st 2021

    have reverted parts of the anonymous edits from rev 6 (which I only just spotted):

    In that edit, the very first sentence of the Idea-section was equipped with a pointer to Sobczyk’s book “New Foundations in Mathematics: The Geometric Concept of Number”.

    But it is out of place here to push that pointer before a single other word has been said, certainly before the pointer to Hestenes’s original book. So I have removed that insertion.

    Generally, while I haven’t looked into that book yet, it is hard not to notice the overblown title. If anyone here has looked into Sobczyk’s book, please let us know what impression you got, and whether it’s a reference worth keeping here.

    diff, v9, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 1st 2021
    • (edited Sep 1st 2021)

    I am also reverting the anonymous edit in rev 8, which, in its entirety, added a pointer to “dyadic rational algebra”.

    Since this is certainly not related to the topic at hand more than any two topics in maths are related, suggesting that this is a “related entry” is at best misleading. If anyone disagrees, then there needs to be discussion in the entry for what the particular relation is meant to be.

    Instead, I have added pointer to the actually related entries, such as Dirac equation and spin geometry.

    [ edit: looking at “dyadic rational algebra” , which is also due to an anonyous contributor, I see from the last line what the intended point is meant to be. Still, this is at best peripheral. If you are the anonymous editor and you are reading this, let me ask that if the link to dyadic rational algebra is to be kept, then it needs to go with a paragraph of explanation, for otherwise it looks out of place ]

    diff, v9, current

    • CommentRowNumber12.
    • CommentAuthorGuest
    • CommentTimeJan 21st 2023
    Re: Geometric Algebra
    Something confusing that I have run across several times on the internet is that the words "Geometric Algebra" are used for "Clifford Algebra" without the unified notation developed by David Hestenes who also uses "Geometric Algebra" to distinguish his formalism from Clifford Algebra notation that was used approximately in the 1960's and 1970's.

    e.g. MIT OpencourseWare: Applied Geometric Algebra text (1976) by László Tisza
    https://ocw.mit.edu/courses/res-8-001-applied-geometric-algebra-spring-2009/resources/mitres_8_001_lec_complete/

    "These notes are a reproduction from original notes provided by Prof. Laszlo Tisza, for Physics
    8.352, Applied Geometric Algebra, offered in the Spring 1976 by the MIT Department of Physics. "
    https://ocw.mit.edu/courses/res-8-001-applied-geometric-algebra-spring-2009/resources/preface/

    Another mechanics book written in the Hestenes unified Geometric Algebra notation:
    http://geocalc.clas.asu.edu/html/NFCM.html
    https://link.springer.com/book/10.1007/0-306-47122-1

1 to 12 of 12

  1.