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It is a well-known phenomenon that mathematicians and physicists working on closely-related topics (say in gauge theories, or in general relativity etc.) generally approach the problems from very different angles and often have trouble understanding each other.

In this light, which book(s) do you wish theoretical physicists working on topics intersecting your own research area had read so they could more readily appreciate your work and/or more easily explain their own work to you in terms accessible to you?

To avoid this being opinion-based, please explain what essential concepts or techniques the theoretical physicist would learn from this book(s).

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    $\begingroup$ I read this Book in 2012-2013 Alexei Kushner, et al. Contact Geometry and Nonlinear Differential Equations amazon.fr/Contact-Geometry-Nonlinear-Differential-Equations/dp/… $\endgroup$
    – user160903
    Commented Sep 16, 2020 at 9:46
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    $\begingroup$ The best Book about Geometry of Quantization I read in 2013-2014 was N. M. J. Woodhouse , Geometric Quantization, amazon.fr/Geometric-Quantization-N-M-Woodhouse/dp/0198502702 $\endgroup$
    – user160903
    Commented Sep 16, 2020 at 9:55
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    $\begingroup$ I recall once hearing a physicist say that all functional analysts should read Dirac's Principles of Quantum Mechanics; he seemed sure that they had not all done so. $\endgroup$
    – Ben McKay
    Commented Sep 16, 2020 at 15:51
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    $\begingroup$ I somewhat dislike the implicit premise of this question, but maybe I am reading too much into it. My very inexpert impression is that theoretical physicists are actually ahead of most of us in using modern techniques. $\endgroup$
    – Mark Wildon
    Commented Sep 17, 2020 at 10:05
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    $\begingroup$ @MarkWildon : I interpret the question to be analogous to a non-native speaker of English asking native English speakers for recommendations for a manual for idiomatic English that is geared toward speakers of English as a second language. $\endgroup$
    – Timothy Chow
    Commented Sep 17, 2020 at 16:50

4 Answers 4

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"Les tenseurs" by Laurent Schwartz. This is the best book on the subject and I often feel that physics books do not really make a good job at presenting tensors. Too bad it has no English translation.

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    $\begingroup$ Maybe I could translate it. $\endgroup$
    – H. de Feraudy
    Commented Sep 22, 2020 at 18:24
  • $\begingroup$ mathoverflow.net/q/17778/88133 $\endgroup$
    – Zach Teitler
    Commented Sep 23, 2020 at 20:39
  • $\begingroup$ @user1741137 that would be great, but I suspect there are rights to be obtained before you can get started. $\endgroup$
    – gmvh
    Commented Sep 28, 2020 at 9:07
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Quantum theory is an application of generalized probability theory (i.e., quantum logic). The most detailed introduction to this approach is: "Geometry of Quantum Theory", by V. S. Varadarajan https://smile.amazon.com/Geometry-Quantum-Theory-V-Varadarajan/dp/0387961240/ref=sr_1_3?crid=7P7GHVPJLJ95&dchild=1&keywords=varadarajan+quantum&qid=1600337321&sprefix=Varadarjan%2Caps%2C194&sr=8-3

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  • $\begingroup$ Second edition: amazon.com/… $\endgroup$
    – gmvh
    Commented Sep 28, 2020 at 9:23
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Nakahara's Geometry, Topology and Physics.

It was chapter $10$ that allowed me to fully engage with connections on fibre bundles and the relationship to Gauge theories. The earlier chapters on Holonomy and de Rham Cohomology groups was instrumental in introducing these concepts from a Physics perspective for me in the early part of my PhD.

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    $\begingroup$ typos, though... $\endgroup$
    – AlexArvanitakis
    Commented Sep 17, 2020 at 11:30
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    $\begingroup$ @AlexArvanitakis Yes, unfortunately this is very true.... $\endgroup$
    – asymptotic
    Commented Sep 22, 2020 at 13:47
  • $\begingroup$ Any hope for a revised edition? $\endgroup$
    – gmvh
    Commented Sep 24, 2020 at 8:27
  • $\begingroup$ There seems to be an unofficial list of errata at www2.physics.ox.ac.uk/sites/default/files/profiles/johnsong/… $\endgroup$
    – gmvh
    Commented Sep 28, 2020 at 9:31
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I always thought spinors were treated in a quite obscure way in physics. In particular it's difficult to make sense of the Dirac adjoint $\bar \psi= \psi^\dagger\gamma_0$ of a spinor (take a look at the wikipedia entry if you don't believe me) until one reads an introductory book on Clifford algebras, particularly one which emphasizes the non-Euclidean case and the natural metric on spinors, like for instance Garling's.

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