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nLab > Latest Changes: higher category theory and physics

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 20th 2010
    • (edited Oct 20th 2010)

    I have been further working on the entry higher category theory and physics. There is still a huge gap between the current state of the entry and the situation that I am hoping to eventually reach, but at least now I have a version that I no longer feel ashamed of.

    Here is what i did:

    • Partitioned the entry in two pieces: 1. “Survey”, and 2. “More details”.

      • The survey bit is supposed to give a quick idea of what the set of the scene of fundamental physics is. It starts with a kind of creation story of physics from ∞\infty-topos theory, which – I think – serves to provide a solid route from just the general abstract concept of space and process to the existence and nature of all σ\sigma-model quantum field theories of “∞\infty-Chern-Simons theory”-type (which includes quite a few) and moreover – by invoking the “holographic principle of higher category theory” – all their boundary theories, which includes all classical phase space physics.

        The Survey-bit continues with indicating the formalization of the result of quantizing all these to full extended quantum field theories. It ends with a section meant to indicate what is and what is not yet known about the quantization step itself. This is currently the largest gap in the mathematical (and necessarily higher categorical) formalization of physics: we have a fairly good idea of the mathematics that describes geometric background structure for physics and a fairly good idea of the axioms satisfied by the quantum theories obtained from these, but the step which takes the former to the latter is not yet well understood.

      • The “More details”-bit is stubby. I mainly added one fairly long subsection on the topic of “Gauge theory”, where I roughly follow the historical route that eventually led to the understanding that gauge fields are modeled by cocycles in higher (nonabelian) differential cohomology.

    • Apart from this I added more references and some cross-links.

    I know that the entry is still very imperfect. If you feel like pointing out all the stuff that is still missing, consider adding at least some keywords directly into the entry.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 20th 2010
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 23rd 2010

    Added sections

    • Phenomenological models: the standard model and gravity

      • Spectral standard model and gravity

      (running out of steam towards the end)

    • References: … On functorial spectral geometry

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2010

    have expanded the paragraph listing examples of (higher) gauge theories to a subsection gauge theory – classes of examples

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 9th 2011

    The opening sentence is not good English

    We discuss the set of the scene of fundamental physics.

    Was the idea to use theatrical terms?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2011

    The opening sentence is not good English

    Okay, thanks. I need to rephrase it then.

    Was the idea to use theatrical terms?

    Yes.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2011

    How about “the backdrop for fundamental physics”? Does that sound weird, too?

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 9th 2011

    The backdrop can suggest it doesn’t structure the action very much. You do say figuratively about a place that it’s a ’stage’. E.g, about the Tower of London

    It has been the stage on which much of England’s dramatic but often sad and bloody saga of royal history has been played out.

    So

    We discuss the stage on which fundamental physics is played out.

    But perhaps setting is better.

    We discuss the setting in which fundamental physics takes place.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2011

    Thanks, David! Very helpful. I have replaced in the entry the sentence with yourr suggestion.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2012
    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 29th 2019

    added pointer to

    diff, v72, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 5th 2020

    added pointer to this recent preprint:

    diff, v73, current

    • CommentRowNumber13.
    • CommentAuthorGuest
    • CommentTimeMar 23rd 2021
    "For a more coherent exposition starting see also at geometry of physics."

    This sentence doesn't make sense! Could it be fixed?
    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMar 23rd 2021

    Thanks for catching this. How about:

    For a more coherent exposition, starting with introduction of the very basics, see also at geometry of physics.

    But one day I’ll want to bring this entry here into better shape…

    diff, v75, current

  15. spelling

    Anonymous

    diff, v77, current

1 to 15 of 15

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