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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2022
    • (edited Jun 9th 2022)

    just re-discovered the existence of the ancienct page holonomic quantum field, while looking to hyperlink the authors of:

    This old page needs attention:

    After I had given (in rev 2) Zoran’s original text the header “Idea”, Zoran complained within the entry (rev 3) about his own text that:

    There is no single mathematical idea expressed here yet!


    Somebody should figure it out

    diff, v5, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 9th 2022

    This article (which I can only see the preview) at least gives us the ’fruit’ of the link:

    Through recent study of the problems in mathematical physics, a deep, unexpected link has emerged: a link between the monodromy preserving deformation theory for linear (ordinary and partial) differential equations, and a class of quantum field operators ([i] [2] [3]). The aim of this article is to give an overview to the present stage of development in the theory (see also [4]).

    The fruit of the above link is multifold. On the one hand it enables one to compute exactly the n point correlation functions of the field in question in a closed form, using solutions to certain non-linear differential equations of specific type (such as the Painlev~ equations). On the other hand it provides an effective new tool of describing the deformation theory by means of quantum field operators. Thus it stands as a good example of the fact that not only the pure mathematics is applied to physical problems but also the converse is true.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2022

    The full text is freely available here.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 9th 2022

    Is there perhaps an Hypothesis H perspective on holonomic field theory? Pure mathematicians are still investigating isomonodromic deformations of such differential equations, as in this tweet.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2022

    If and in as far as it’s related to the KZ-equation the answer would be “yes” (that’s the content of Anyonic Defect Branes).

    However, I haven’t even opened any article on “holonomic field theory” yet, so I don’t know what exactly that term subsumes.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeJun 12th 2022
    • (edited Jun 12th 2022)

    @1 I did not complain about the text, nor your formatting into paragraphs, but merely left a reminder about calling the vague orientation what this subject is about “idea”. Idea of the construction is yet to be written.

    I think the title of the paragraph as it is now reminds us temporarily and honestly that the true idea of the construction is on our to do list. Once the essence of the construction is outlined we can rename the entire intro section into “Idea”. I highly respect this subject but somehow miss the clarity to explain it yet.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2022

    I’d suggest to remove the lines “There is no single mathematical idea expressed here yet!” and “Idea: Somebody should figure it out”. Instead we could just write “under construction” at the top of the page.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2022

    I have now deleted these two lines.

    Then I have added the quote given by David C. in #2.

    Also started fixing the bibitems and their hyperlinking, but I give up now, for the moment.

    diff, v6, current