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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 30th 2013

    started something at twistor space

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 31st 2013
    • (edited Oct 31st 2013)

    added a section twistors for 4d Minkowski spacetime with basics on the actual original definition and motivation for twistors.

    (from looking around I gather this is now the only discussion on the web that comes out right away with admitting what a twistor actually is, conceptually :)

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 18th 2016

    added an actual section twistor space with discussion of how 𝕂P 3\mathbb{K}P^3 encodes light-like geodesics in Minkowski spacetime. Did this in the generality that 𝕂{,,}\mathbb{K} \in \{\mathbb{R}, \mathbb{C}, \mathbb{H}\}, hence for Minkowski spacetime of total dimensions 3,4, and 6, in order to amplify the algebraic pattern.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 18th 2016

    To discuss twistor space for Minkowski spacetime, it is useful to work more generally with dd-dimensional Minkowski spacetime for d{3,4,6,8}d \in \{3,4,6,8\}.

    Do you mean 10 rather than 8?


    …vectors in Minkowski spacetime in d={2,3,4,10}d = \{2,3,4,10\}

    why those dimensions?

    For d=10d = 10 there is no elegant statement like this, due to the non-associativity of the octonions

    There’s plenty of discussion about why there can’t be an 𝕆P 3\mathbb{O} P^3 here. Enough associativity for 𝕆P 2\mathbb{O} P^2, but not projective space. Does the lack of octonion spinors tell us anything, or is it just an inconvenience?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 18th 2016
    • (edited Oct 18th 2016)

    Sorry for the silly typos, fixed now. Thanks for catching them. I’ll try to catch the next train home to get some sleep.

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 14th 2018

    Corrected a subscript.

    diff, v36, current

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