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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeMay 18th 2010
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 18th 2010

    soon after filling it, nlab ceased to work

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeMay 18th 2010

    Now it works and I added more subsections.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 18th 2010

    Thanks, Zoran, very nice indeed!

    I put in some more links, and also a TOC. For that I had to move the hyperlinks out of the section titles into the text. Hope you don’t mind. I think a toc for such a long list is very useful.

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeMay 18th 2010

    Of course I don’t mind, but thanks for explaining as it did not make sense to me why repeating the same words from the title in the first sentence after it :) I was answering a MO question where somebody asked about references on mathematical physics and then I epxanded my answer a bit and voila, a useful nlab entry :) I feel a bit healthier today, though still fragile.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 18th 2010

    I could tell you were feeling more vigorous today, Zoran! That’s good news – keep getting better. Rest!

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeMay 18th 2010
    • (edited May 18th 2010)

    I do one disciplined thing these days: do not let myself stay up late in the evening. If the health does not let me sleep in bed I can not protest, but at least I go to bed early enough. And I am far more careful with food and not getting into too exhaustive endeavours beyond my present capacities. Thanks.

    • CommentRowNumber8.
    • CommentAuthorIan_Durham
    • CommentTimeMay 18th 2010
    I don't know if this is appropriate for the types of books you wish to list there, since it takes sort of the opposite approach - teaching math to physicists - but it is a much more "mathematical" book than its competitors. If it is worth adding, I will do so:

    Mathematics for Physics and Physicists, Walter Appel, Princeton University Press.
    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    I would not add it. Minor book with minor originality from a minor author in my memory (I do not hqave a file or copy to look again to see what is it worth). I would like to have a wide choice, but not getting into minor college authors.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2010

    Yes. And Math for Physicsists is not Mathematical Physics.

    • CommentRowNumber11.
    • CommentAuthorIan_Durham
    • CommentTimeMay 19th 2010
    OK.

    And Math for Physicsists is not Mathematical Physics.



    Yes, I said that:

    it takes sort of the opposite approach



    Minor book with minor originality from a minor author in my memory (I do not hqave a file or copy to look again to see what is it worth). I would like to have a wide choice, but not getting into minor college authors.



    Where he teaches shouldn't matter. It's an excellent, well-written book that is a badly needed update on the standard "mathematical methods" text.
    • CommentRowNumber12.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    Where he teaches shouldn’t matter.

    There has been a lot of discussion about this in mathematics literature. Most of the authorities agree that to write a good advanced mathematical monograph one of the prerequisites is to have a significant contribution to the area. There are exceptions as to any rule of thumb, but most of the time, a sensitive researcher can easily find what aspects makes some monograph in their area superficial or not to the point.

    • CommentRowNumber13.
    • CommentAuthorTim_van_Beek
    • CommentTimeMay 19th 2010

    Is GR left out on purpose? (If you say: “Yes, as a mathematically rigorous and well established theory it is just too easy to find good books” I would agree ;-)

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2010

    Is GR left out on purpose?

    Go ahead, Tim!

    • CommentRowNumber15.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    I would suggest to open a separate subsection to nonobsolete major mathematical monographs on GR if you are able to compose such. For the level of rigor of theoretical physics I would suggest a separate entry (then things starting from say Landau’s vol2, field theory go on…). The book on Wells and Wald on twistors has some prerequisites for some of the relevant topic. Part of GR is covered by differential geometry books like the famous adn encyclopaedic monograph of Besse “Einstein manifolds”. The book of Misner et al is certainly not mathematical physics but theoretical physics book discussing all kinds of aspects from history to experiment and heuristics of cosmological models.

    • CommentRowNumber16.
    • CommentAuthorTim_van_Beek
    • CommentTimeMay 19th 2010

    I’ll try, but I do not like to list books that I did not have one single look at, and that includes for example “Einstein manifolds”…

    • CommentRowNumber17.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010
    • (edited May 19th 2010)

    Right, one should not list books by copying their unwarranted fame, and multiply the common misconceptions. In such restricted list it is better to temporarily omit some and to list those one really feels compelled to include. For Einstein manifolds, I can do the addition with quite a lot of assuredness that I am not making a mistake in that particular case.

    • CommentRowNumber18.
    • CommentAuthorTim_van_Beek
    • CommentTimeMay 19th 2010

    Okay :-) I added my list of GR books and I added JB’s books list in the books list list.

    • CommentRowNumber19.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    I compacted it a bit and added Besse. I am a bit uncomfortable with recommending Chandrasekhar, I mean much of the book has excessive details of obsolete importance while the core worthy part is included in more modern books. I know that it is historically hugely famous, and still readable to physicists. But you are more exprienced in that area so I can believe your judgement that it may be still worthy to quote as a reference (but not as textbook!).

    I avoid to list books on affine Lie algebras and quantum groups in the list, as this literature is extensive (with lots of important books) and can be given separately as a special topic; however I included Pressley and Segal on loop groups because of huge influence to the whole subject of mathematical physics and clear style: positive energy representations, Segal Grassmanian for integrable systems, geometrical notion of a blip (vertex operator)…

    • CommentRowNumber20.
    • CommentAuthorTim_van_Beek
    • CommentTimeMay 19th 2010

    But you are more exprienced in that area…

    I doubt that, I never did serious research in GR.

    I am a bit uncomfortable with recommending Chandrasekhar…

    You’re right, certainly not as a textbook! I included it because it contains extensive analytical calculations, which normally don’t get published at all, only the results are. Or the conceptual insights. But for some people, this is what they do all day long! (Hubert Gönner in Göttingen is a computing machine, I still suspect they feed him microchips in secret). One remark is particularly charming, citing from memory: “the detailed calculations cannot be included, for they are too long, but the interested reader can take a look at several notebooks of mine in the library at the university of Chicaco”.

    • CommentRowNumber21.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    Wow this is an impressive procedure: puttingthe notebooks in a library. Reminds a bit of nlab. I know R. Thomason is famous for his long chain of 120-page-numbered notebooks. Count Wodzicki has told me he started keeping ordered notebooks from a while ago. But it does not look like they will be public soon, though they contain lots of unknown theorems.

    • CommentRowNumber22.
    • CommentAuthorTim_van_Beek
    • CommentTimeMay 19th 2010

    Charming, isn’t it? If I ever get to Chicaco in my life, I will try to take the time to find those :-)

    Nevertheless I removed the reference to Chandrasekhar and added Araki on AQFT and Howard Georgi: “Lie Algebras in Particle Physics. From isospin to unified theories.” instead.

    • CommentRowNumber23.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    Well this Chandrasekhar reference should be still kept somewhere in nlab, maybe in some specialized entry on general relativity. If not the main list of math physics canonical texts, it should be somewhere.

    • CommentRowNumber24.
    • CommentAuthorTim_van_Beek
    • CommentTimeMay 19th 2010

    I certainly won’t forget it, but my focus is not on GR, but on AQFT and trying to understand some category theory…if I start writing about GR here I’ll be consumed by context switches :-)

    • CommentRowNumber25.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    OK, I copied your record of the book into a new person entry Subrahmanyan Chandrasekhar.

    • CommentRowNumber26.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010

    I added Weinberg’s vol 3 as a reference to supergravity entry and reorganized refs. there a tiny bit.

    • CommentRowNumber27.
    • CommentAuthorIan_Durham
    • CommentTimeMay 19th 2010
    I fixed a minor typo (someone had typed "Thorpe" and not "Thorne").

    Note: probably not appropriate for that list, but from a historical standpoint, Eddington's first English text on the subject was considered a masterpiece.
    • CommentRowNumber28.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2010
    • (edited May 19th 2010)

    Thanks for the Thorpe/Thorne.

    Eddington’s text is not in the manner of a mathematical physics text, and from a point of theoretical physics had few conclusions which are now considered wrong.

    • CommentRowNumber29.
    • CommentAuthorIan_Durham
    • CommentTimeMay 19th 2010
    Which is why I said it probably wasn't appropriate. Nevertheless, it was the first English-language text on the subject and Einstein himself considered it one of the finest expositions of GR.

    Note that a lot of Eddington's more technical writing does border on mathematical physics. He was an early pioneer on the use of Clifford algebras in physics and independently discovered Majorana spinors.
  1. I added a link to Kapustin's survey, but I did not know how to name the link, so I just called it arxiv (maybe arxiv:math-qa:1004.2307 would have been better?).

    Professor Warner http://www.math.washington.edu/~warner/ has some pdf files that _look_ related. However, I have not read a single one, so I can not really judge that.
    • CommentRowNumber31.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2010
    • (edited May 19th 2010)

    maybe in some specialized entry on general relativity

    you should create general relativity and start a References-section there. Also special relativity (for which a stub now exists) could do with a good References-list

    • CommentRowNumber32.
    • CommentAuthorzskoda
    • CommentTimeMay 20th 2010
    • (edited May 20th 2010)

    Kapustin survey is not an unavoidable survey for a list of main references in mathematical physics. It is quite partial just for some aspects and just one of the about 100 surveys in string and QFT theory and I listed it before in entry Anton Kapustin. For example, the book by Turaev is much more historically representative and comprehensive, though it is a bit old now and hence does not have the Lurie stuff. The intention in preparing the list is just to include those references which one is compelled to include, those one can not do without. Not all the useful references, but just the choice one can recommend to a person willing to choose some areas in mathematical physics for serious study or reference in the shelf. With some hesitation I have included Sati’s survey though as it is rather comprehensive and quite in focus of the research of some people in nlab.

    Yes, naming arxiv:1004.2307 is better as it gives a unique reference. Just arxiv, is not a reference, but a place to search.

    • CommentRowNumber33.
    • CommentAuthorzskoda
    • CommentTimeMay 20th 2010

    I have added the arxiv number at the Kapustin ICM talk, which can stay there until we find a good replacement at least. I will open a separate page for Landau-Lifschitz course of theoretical physics.

    • CommentRowNumber34.
    • CommentAuthorzskoda
    • CommentTimeJul 9th 2010
    • CommentRowNumber35.
    • CommentAuthorUrs
    • CommentTimeJul 9th 2010
    • (edited Jul 9th 2010)

    New entry books about string theory

    Thanks, nice! I moved the link to that to the very top of the references section at string theory.

    Somehow the textbook on string theory that does the subject justice has not been written yet. But some day I guess it will…

    • CommentRowNumber36.
    • CommentAuthorzskoda
    • CommentTimeJul 9th 2010

    From the present day standards, no one does the justice, so one can imagine what needs to be done to write such a book. But by that time, there will be so much more new misterius aspects, that from that point of view won-t be a justice again… :)

    • CommentRowNumber37.
    • CommentAuthorUrs
    • CommentTimeJul 9th 2010

    right, but i think there is not even a really good book about those aspects that are fairly clear. most of the textbooks greatly overstrain themselves by trying to start with the harmonic oscillator on page 3 and somehing completely not understood on page 300.

    one could see this very well in polchinki’s book, which was probably the string textbook in the physics-style league with the most sophistication: after book 1 gave a decent discussion of many cft topics, physics-style, book 2 was a rather breathless tour de force through concepts that would have required something else.

    anyway, at some point it will be written. after all, the really decent perturbative qft books are also still to come. the one on costello’s website looks promising…

    • CommentRowNumber38.
    • CommentAuthorzskoda
    • CommentTimeOct 15th 2010
    New stub hydrodynamics with temporary redirect for wider area fluid dynamics.
    • CommentRowNumber39.
    • CommentAuthorzskoda
    • CommentTimeOct 15th 2010
    • (edited Oct 15th 2010)

    One of the references I cite at hydrodynamics is a new arXiv article

    At the end of the article, Sullivan hints of a need to enhance the infinite-categorical/derived geometry which includes more than a BV algebra, namely certain pairings from hydrodynamics are missing in order to be able to well-organize computational models of fluids. This means that he alludes to a exciting new and direct practical use of higher category theory. He says Costello's work on renormalization is close but not quite up to express the foundational step which is missing to go toward that theory.

    • CommentRowNumber40.
    • CommentAuthorzskoda
    • CommentTimeJul 31st 2013
    • (edited Jul 31st 2013)

    I have removed the section Classical mechanics from this entry as it is represented in section “Geometry and symmetries in classical and QM, but not much QFT” where all books focusing on classical and semiclassical picture are listed like Arnold, Spivak, Sternberg, Landsman…Most books which deal with geometry of classical mechanics mathematically profoundly deal wth quantization or alike structures so are not limited to classical mechanics this is why it makes sense to put those together.

    Edit: renamed to Classical mechanics and possibly quantization and symmetries of QM (but no QFT)

    • CommentRowNumber41.
    • CommentAuthorzskoda
    • CommentTimeJul 31st 2013

    O kind of reorganized back, with some changes, but not entirely happy. Classical mechanics is hard to seperate from quantzation, symmetries and geometry, unless one lists the physics mechanics textbooks of old kind which are written without differential geometry and emphasis on symmetries. So I have now classical mechanics separated but not happy with this.

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