What are you reading now? (STEM only)

[fresh_42]

I don't think we have actually ran out of problems at all

With respect to descriptive methods? Of course we have enough problems, but neither requires new methodical mathematics as far as we know. We discuss whether the small Lie groups need to be replaced by larger ones, we grade Lie algebras for string theory, we even use cohomology, and of course all takes place on Riemannian manifolds with sometimes strange pseudo metrics like Minkowski, or very difficult differential equations like Navier-Stokes. However, all those things can easily be described by what we have. In this sense physics ran out of problems as a necessity to build new branches in mathematics.

 

[atyy]

With respect to descriptive methods? Of course we have enough problems, but neither requires new methodical mathematics as far as we know. We discuss whether the small Lie groups need to be replaced by larger ones, we grade Lie algebras for string theory, we even use cohomology, and of course all takes place on Riemannian manifolds with sometimes strange pseudo metrics like Minkowski, or very difficult differential equations like Navier-Stokes. However, all those things can easily be described by what we have. In this sense physics ran out of problems as a necessity to build new branches in mathematics.

How about the KPZ equation? I think even Landau damping was not firmly founded until recently. And 4D QFT is still undefined.

KPZ: https://arxiv.org/abs/1109.6811
Landau damping: http://smai.emath.fr/cemracs/cemracs10/PROJ/Villani-lectures.pdf
4D QFT: https://www.claymath.org/millennium-problems/yang–mills-and-mass-gap

 

[DaveC49]

Evolution The Whole Story Ed Steve Parker (https://thamesandhudson.com/evolution-the-whole-story-9780500291733)
Selected papers on Quantum Electrodynamics julian Schwinger (https://store.doverpublications.com/0486604446.html) historical persepective on development of QED.

 

[atyy]

https://mitpress.mit.edu/books/broken-movementBroken Movement: The Neurobiology of Motor Recovery after Stroke
By John W. Krakauer and S. Thomas Carmichael

https://www.cambridge.org/core/book...tter-physics/F0A27AC5DEA8A40EA6EA5D727ED8B14EModern Condensed Matter Physics
By Steven M. Girvin and Kun Yang

Girvin and Yang's book was mentioned by @fluidistic in the STEM Bibles thread.

 

[martinbn]

Don't know if this counts, but since Landau damping was mentioned it reminded me that I just finished Cedric Villani's "Birth of a Theorem: A Mathematical Adventure".

 

[Auto-Didact]

Don't know if this counts, but since Landau damping was mentioned it reminded me that I just finished Cedric Villani's "Birth of a Theorem: A Mathematical Adventure".

How was it? Been following him for awhile now.

Landau damping is perhaps the best example of an extremely broad mathematical model with applications going far beyond just physics. AFAIK, the mathematical theory hasn't been fully understood yet, with the still uncovered underlying mathematics remaining a breeding ground for novel forms of mathematical unification.

 

[martinbn]

How was it? Been following him for awhile now.

Landau damping is perhaps the best example of an extremely broad mathematical model with applications going far beyond just physics. AFAIK, the mathematical theory hasn't been fully understood yet, with the still uncovered underlying mathematics remaining a breeding ground for novel forms of mathematical unification.

It is good, but I don't think that anyone who is not already familiar with how math/science is done will get the right impression. I can imagine someone saying "I know exactly how he feels, it was the same for me when I was studying for my calc 101 midterm."

 

[Lynch101]

I made an attempt to read the Problem of Time: Quantum Mechanics versus General Relativity by Dr. Edward Anderson. Unfortunately, I don't have any mathematical background, so the majority of it was over my head, but I was still able to get a lot out of it.

It's a very comprehensive breakdown of the Problem of Time (PoT) in Qunatum Gravity. It looks at the different facets of the PoT and how each proposed theory attempts to address them. It draws on earlier reviews of the PoT by Isham and Kuchaˇr.

 

[MathematicalPhysicist]

Just reading Grensing, Structural Aspects of Quantum Field Theory (2 volumes, more than 1600 pages).

I assume it's another take of a mathematician of QFT.

Have you read Zeidler's three volumes on QFT?
I think he he wanted to publish another more two volumes on QFT, but unfortunately he died in 2016 before publishing them.

 

[Demystifier]

I assume it's another take of a mathematician of QFT.

Have you read Zeidler's three volumes on QFT?
I think he he wanted to publish another more two volumes on QFT, but unfortunately he died in 2016 before publishing them.

Zeidler is much more mathematical than Grensing. I didn't like Zeidler for the reason that his books are a mess; the chapters, sections and subsections do not seem to be ordered logically.

 

[MathematicalPhysicist]

Zeidler is much more mathematical than Grensing. I didn't like Zeidler for the reason that his books are a mess; the chapters, sections and subsections do not seem to be ordered logically.

Can you elaborate on what is not logical in the ordering?

 

[George Jones]

I assume it's another take of a mathematician of QFT.

Have you read Zeidler's three volumes on QFT?

Zeidler is much more mathematical than Grensing. I didn't like Zeidler ...

With respect to maths books on QFT, I like Follands's book, and I await with with eager anticipation the publication of Michel Talagrand's book. It appears that Talagrand subscribes to Victor Weisskopf's"uncover a little" as opposed to "cover a lot" philosophy of pedagogy; see the Table of Contents and Introduction to Talagrand's book:

http://michel.talagrand.net/qft.pdf

 

[MathematicalPhysicist]

With respect to maths books on QFT, I like Follands's book, and I await with with eager anticipation the publication of Michel Talagrand's book. It appears that Talagrand subscribes to Victor Weisskopf's"uncover a little" as opposed to "cover a lot" philosophy of pedagogy; see the Table of Contents and Introduction to Talagrand's book:

http://michel.talagrand.net/qft.pdf

I have both Ticciati's and Folland's as well.
I find it quite amazing that you can find insights on the subject (QFT) from several different authors. It just tells you how vast this subject is.
Sometimes I think that every mathematical tool is being used in QFT and quantum gravity theories.
Which is great, but hard to grasp it in a few years.

 

[Demystifier]

Can you elaborate on what is not logical in the ordering?

Example 1: The second book is called "Quantum Electrodynamics", but actual quantum electrodynamics starts at the page 771.

Example 2: Special relativity is treated in detail in the third book called "Gauge Theory" (Chapters 18-20), while it would be much more logical to treat it in the first book called "Basics in Mathematics and Physics".

Do yo want more?

 

[MathematicalPhysicist]

Example 1: The second book is called "Quantum Electrodynamics", but actual quantum electrodynamics starts at the page 771.

Example 2: Special relativity is treated in detail in the third book called "Gauge Theory" (Chapters 18-20), while it would be much more logical to treat it in the first book called "Basics in Mathematics and Physics".

Do yo want more?

Well for example 1, I guess he covers all the mathematics that one needs to know before tackling QED which sounds to me reasonable; the same with example 2.

What would you prefer? first giving you all the physics combined with the necessary math, or first the math and then the physics.

It doesn't sound to me as a terrible choice that he had done.
It's not like Peskin and Schroeder that they pour on you the math with the physics, and you don't understand what are the exact mathematical definitions they are using.

But yes, SR should be before QED.

 

[Demystifier]

Well for example 1, I guess he covers all the mathematics that one needs to know before tackling QED which sounds to me reasonable; the same with example 2.

He also covers a lot of math that he does not use in actual QED at all.

 

[MathematicalPhysicist]

He also covers a lot of math that he does not use in actual QED at all.

What for example?
Surely not any set theory and mathematical logic there, right?

 

[Demystifier]

What for example?
Surely not any set theory and mathematical logic there, right?

For example, Chapter 4 on equivalence classes is not used in the actual QED part.

Some additional examples. Chapter 4 (of the second book) is nominally about equivalence classes, but Secs. 4.5 and 4.6 have noting to do with equivalence classes.

 

[George Jones]

For example, Chapter 4 on equivalence classes is not used in the actual QED part.

Equivalence classed are used in QED for Gupta-Bleuler quantization. Zeidler defines the relevant space of equivalence classes somewhat implicitly and very briefly in the last line of page 830. The brief book "Quantum Mechanics and Quantum Field Theory: A Mathematical Primer" by Dimock define the quotient space of equivalence classes more explicitly.

 

[fresh_42]

Equivalence classes are hidden everywhere: Cauchy sequences for completeness of Hilbert spaces, various representations of the SU groups as quotient groups, outer product spaces etc.

 

[Demystifier]

So is there someone here who thinks that organization and ordering in the Zeidler QFT books is not a mess?

 

[George Jones]

So is there someone here who thinks that organization and ordering in the Zeidler QFT books is not a mess?

I strongly suspect that you are right about this, but I find Zeldler's 3000+ pages to be so overwhelming that, even though all three volumes are on my shelf, I have made no systematic attempt to read large portions of them. I have read read selected small portions.

 

[jordi]

So is there someone here who thinks that organization and ordering in the Zeidler QFT books is not a mess?

I agree. In fact, volume I was better organized. Of course I do not know, but it could be that Zeidler was becoming old and tired (he passed away a few years ago, without publishing the 4th, 5th and 6th promised volumes).

Also, he promised some things in volume 2 and 3 (in volume 1), and he did not deliver.

It is a pity, because his intentions were really good, I liked his style a lot.

 

[Demystifier]

I think the Zeidler's QFT books should be retitled as:
Some Aspects of Mathematics, Physics and Their Interrelationship with an Ariadne Thread in Quantum Field Theory

More seriously, I think his books should not be read as textbooks, but rather as a series of review papers.

 

[George Jones]

More seriously, I think his books should not be read as textbooks, but rather as a series of review papers.

Yes, e.g.,
https://www.physicsforums.com/threads/continuous-eigenvalues.428384/#post-2880479

 

[Demystifier]

Yes, e.g.,

And your signature is particularly valid for the Zeidler's books. One should not read them linearly from cover to cover, instead one should skim over the Contents and pick (sub)sections that make one feel curious at the moment.

 

[CosmicEgyptian19]

I am reading a book called Idiot's Guide to Quantum Physics by Marc Humphrey and some other people. I became interested in this topic after learning about the double slit experiment. This is also my first answer to something on this website, did I do it right?

 

[doggydan42]

I'm reading Sakurai's Quantum Mechanics and an Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee.

 

[Jimster41]

“Quantum Field Theory of Many Body Systems”
Xiao-Gang Wen

That is to say I have understood and enjoyed both the preface and first chapter... that may well be all.

 

[member 587159]

I'm currently reading Abstract Algebra by Dummit and Foote to expand my knowledge on abstract algebra. It is a great book which I can recommend. It contains many examples, tricks, and highlights what is really important to remember. It has too many exercises to make them all, so I pick the ones that seem more interesting or harder.

Currently, I am at p145 which deals with groups and the Sylow theorems. I hope to get to ring theory soon and if there is time left I hope to begin with module theory.

 

[Klystron]

I visit my local library once a week usually picking up books I reserve online. Today with no books on hold I revisited a method from childhood by wandering in the Science and Math section looking for books I have not read recently. The stacks were full as most local schools are on Summer hiatus.

I chose "The Magic Of Math" by Arthur Benjamin and "The Island of Knowledge" by Marcelo Gleiser for summer reading then was bemused to find a 2001 Cambridge Press math textbook by an author familiar to us all on Physics Forums. I added "Introduction to Numerical Analysis" by Arnold Neumaier. @A. Neumaier , I presume?

[Later feedback: "The Magic of Math" is a highly readable gateway to counting and combinatorics among other subjects. "Island of Knowledge" seems aimed at beginning knowledge engineers and students of epistemology. "Intro to Numerical Analysis" is a focused comprehensive overview of the field as the title promises and the author delivers.]

 

[A. Neumaier]

I visit my local library once a week usually picking up books I reserve online. Today with no books on hold I revisited a method from childhood by wandering in the Science and Math section looking for books I have not read recently. The stacks were full as most local schools are on Summer hiatus.

I chose "The Magic Of Math" by Arthur Benjamin and "The Island of Knowledge" by Marcelo Gleiser for summer reading then was bemused to find a 2001 Cambridge Press math textbook by an author familiar to us all on Physics Forums. I added "Introduction to Numerical Analysis" by Arnold Neumaier. @A. Neumaier , I presume?

Yes. Happy reading!

 

[MidgetDwarf]

Yes. Happy reading!

From the book description on Amazon and the few pages I was able to read. The book looks promising. Does is it presuppose knowledge of Complex Analysis (the one a math major takes (pure)) as a prerequisite?

 

[A. Neumaier]

From the book description on Amazon and the few pages I was able to read. The book looks promising. Does is it presuppose knowledge of Complex Analysis (the one a math major takes (pure)) as a prerequisite?

Not for most of the material, only for the derivation of a few details.

 

[MidgetDwarf]

Not for most of the material, only for the derivation of a few details.

Thank you for replying. Will start reading it in December.