Mathematics for Physics by Adam Marsh

[atyy]

Adam Marsh's Mathematics for Physics is available online. Subodh Patil recommends the algebraic topology section, and as a primer to Nakahara.

 

[Demystifier]

Adam Marsh's Mathematics for Physics is available online.

I think the title of the book is misleading, because it's mainly geometry and topology for physics.

Which reminds me of another book with a misleading title:
https://www.amazon.com/dp/B084GMNHCQ/?tag=pfamazon01-20
Despite the title, the book says nothing about classical mechanics, only little about quantum field theory, while the emphasis is on the mathematics for non-relativistic QM which is not mentioned in the title at all.

 

[malawi_glenn]

I think the title of the book is misleading

I always scrutinize table of contents in all of those "mathematical methods for physics" books. Same with books that just read "Field theory" - what fields do they discuss and classical / quantum

 

[martinbn]

Adam Marsh's Mathematics for Physics is available online. Subodh Patil recommends the algebraic topology section, and as a primer to Nakahara.

What are some examples where algebraic topology is needed in physics?

 

[martinbn]

I think the title of the book is misleading, because it's mainly geometry and topology for physics.

Well, it doesn't say all mathematics. It just says mathematics, and geometry and topology is mathematics.

 

[vanhees71]

I'd say 99.9% of the mathematics you need in physics is geometry ;-).

 

[Demystifier]

I'd say 99.9% of the mathematics you need in physics is geometry ;-).

It doesn't make sense. Take, for example, non-relativistic QM. A lot of algebra, a lot of analysis, in more mathematical treatments a lot of functional analysis, but very little geometry.

 

[malawi_glenn]

What are some examples where algebraic topology is needed in physics?

Topological solitions (defects) and such. https://theconversation.com/the-nob...-to-topology-and-mathematicians-applaud-66532

Otherwise: gauge theory (Yang-Mills) string theory

https://arxiv.org/abs/1304.7846

 

[martinbn]

Topological solitions (defects) and such. https://theconversation.com/the-nob...-to-topology-and-mathematicians-applaud-66532

Is there any algebraic topology here?

Otherwise: gauge theory (Yang-Mills) string theory

https://arxiv.org/abs/1304.7846

Where is the physics?

 

[malawi_glenn]

Where is the physics?

Right, I forgot that string theory and Yang-Mills is not physics, my bad. I will now put my Nakahara book in the paper recycling bin.

Are you asking because you want to know, or are you critical (skeptical)? You think algebraic topology in physics is like the Emperors new clothes?

Is there any algebraic topology here?

Isn't topological defects and topological charges studied in algebraic topology, or are you suggesting that general topolgy is enough for those applications?

 

[Demystifier]

Well, it doesn't say all mathematics. It just says mathematics, and geometry and topology is mathematics.

So, do you think that the title is well chosen?

 

[vanhees71]

It doesn't make sense. Take, for example, non-relativistic QM. A lot of algebra, a lot of analysis, in more mathematical treatments a lot of functional analysis, but very little geometry.

This is just the framework you need to realize the geometric content of the physics. The operator algebra defining non-relativistic QM follows directly from the symmetry properties of the non-relativistic spacetime model.

 

[martinbn]

Right, I forgot that string theory and Yang-Mills is not physics, my bad. I will now put my Nakahara book in the paper recycling bin.

I was asking about the paper you linked to. It seemed like an introduction to algebraic topology, but i didnt see any physics.

Are you asking because you want to know, or are you critical (skeptical)? You think algebraic topology in physics is like the Emperors new clothes?

I am asking because i would like to see some examples.

Isn't topological defects and topological charges studied in algebraic topology, or are you suggesting that general topolgy is enough for those applications?

I don't know. The article about the Noble prize didnt have much detail.

 

[malawi_glenn]

It seemed like an introduction to algebraic topology, but i didnt see any physics.

It mentions several physical applications, but do not discuss them in lenght.

I am asking because i would like to see some examples.

indirectly you classified Yang-Mills and string theory as not physics here.

 

[martinbn]

It mentions several physical applications, but do not discuss them in lenght.

I suppose I have to read the article in detail. I must have missed them.

View attachment 303805
indirectly you classified Yang-Mills and string theory as not physics here.

But I didn't see them in the article. Hence my question. You could cite the pages. That was my question "where is the physics?".

 

[malawi_glenn]

But I didn't see them in the article

I did not mean that that article was a source for Yang Mills and string theory but just as source with more examples.

Anyway, my list of examples of algebraic topology in physics are:
- Topological defects/invariants
- Yang Mills (non abelian gauge theory)
- String Theory
These are the ones that comes to my mind.

 

[malawi_glenn]

I guess there are some applications in general relativity as well, but I am not that much into that field

Anyway, I thought the thread was about this online "book", not what applications algebraic topolgy has in physics.

 

[martinbn]

I did not mean that that article was a source for Yang Mills and string theory but just as source with more examples.

But can you point the pages with those examples, so that I don't have to read the whole thing. I just couldn't find them.

Anyway, my list of examples of algebraic topology in physics are:
- Topological defects/invariants
- Yang Mills (non abelian gauge theory)
- String Theory
These are the ones that comes to my mind.

That is great but I want to see something specific. Saying any of those areas, say string theory, is way too broad. What are some examples from string theory (or anything else) that uses algebraic topology? That's what I am curious to see.

 

[martinbn]

I guess there are some applications in general relativity as well, but I am not that much into that field

This would be even more interesting for me to see. Anyone?

Anyway, I thought the thread was about this online "book", not what applications algebraic topolgy has in physics.

Yes, may be this is for a separate thread, but the book has algebraic topology in it as part of mathematics used/needed in/for physics. It is somewhat on topic to ask for some examples, may be from the book itself.

 

[malawi_glenn]

It is somewhat on topic to ask for some examples, may be from the book itself

Don't you think the chances are greater if you make a dedicated thread about it that people will notice and reply? The book is also quite broad, it covers more math than just algebraic topology.

Imagine a thread about a book on nuclear physics, should there be discussion of applications of radioactive decays in the same thread? I do not think so. Better to ask what applications of radioactive decays are discussed in that book.

I could not see any explicit examples of physics in the algebraic topology book by Marsh, I just glanced over that chapter.

This would be even more interesting for me to see. Anyone?

https://arxiv.org/abs/gr-qc/9509048v1

 

[atyy]

It doesn't make sense. Take, for example, non-relativistic QM. A lot of algebra, a lot of analysis, in more mathematical treatments a lot of functional analysis, but very little geometry.

Collapse is projection, which is geometry

 

[martinbn]

Collapse is projection, which is geometry

Or algebra?
https://en.wikipedia.org/wiki/Projection_(linear_algebra)

 

[malawi_glenn]

@martinbn this of one of my first exposures to homotopy and abstract algebra https://arxiv.org/abs/0908.1395 you might find some neat examples in there

 

[malawi_glenn]

So, do you think that the title is well chosen?

"Geometrical and topological methods for theoretical physics - an illustrated handbook"
would have been my choice

 

[martinbn]

@martinbn this of one of my first exposures to homotopy and abstract algebra https://arxiv.org/abs/0908.1395 you might find some neat examples in there

That's quite long. Can you pinpoint some of the examples?

 

[malawi_glenn]

That's quite long. Can you pinpoint some of the examples?

What own research and effort have you made to answer your question "what are some examples of applications of algebraic topology in physics"? For someone with these many posts and likes, I would assume that you know you have to show some own effort and just not be spoonfed by others?

 

[martinbn]

What own research and effort have you made to answer your question "what are some examples of applications of algebraic topology in physics"? For someone with these many posts and likes, I would assume that you know you have to show some own effort and just not be spoonfed by others?

! It was just a question, out of curiosity. If there was someone who knew the answer, he could just tell me. If not, then it is my problem to search and satisfy my curiosity. If you think it is off topic, or you don't have anything specific that you can point to out of the top of your head, you can just not reply to me.

 

[Son Goku]

What are some examples where algebraic topology is needed in physics?

Many strong force particles get contributions to their mass from classical Yang-Mills solutions weighted by their Chern class. Eta prime is an example.

 

[MathematicalPhysicist]

I didn't read all the posts in this thread, but do you know if the third edition will have a hard copy version of Mikio Nakahara's?

 

[MathematicalPhysicist]

I can see the publication date on amazon of the paperback is: https://www.amazon.ae/Geometry-Topology-Physics-Third-Nakahara/dp/1439840717 23rd of September.

With your experience a book's worth diminishes with time or exceed, by the price of it?

 

[malawi_glenn]

23rd of September.

in 2023

 

[MathematicalPhysicist]

in 2023

ah yes...Too much work of grading students' work.

 

[MathematicalPhysicist]

ah yes...Too much work of grading students' work.

Though the author can postpone the publication to 2030...

 

[malawi_glenn]

Though the author can postpone the publication to 2030...

The list of errata from the second edition must be worth two entire books I guess!

 

[Unique_Engineer]

The list of errata from the second edition must be worth two entire books I guess!

It looks like he postponed it again to 2027...
https://www.amazon.com.be/-/en/Mikio-Nakahara/dp/1439840717
Believe me in the end it will be in 2030...

Cheers!