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Adam Marsh's Mathematics for Physics is available online. Subodh Patil recommends the algebraic topology section, and as a primer to Nakahara.
I think the title of the book is misleading, because it's mainly geometry and topology for physics.Adam Marsh's Mathematics for Physics is available online.
I think the title of the book is misleading
What are some examples where algebraic topology is needed in physics?Adam Marsh's Mathematics for Physics is available online. Subodh Patil recommends the algebraic topology section, and as a primer to Nakahara.
Well, it doesn't say all mathematics. It just says mathematics, and geometry and topology is mathematics.I think the title of the book is misleading, because it's mainly geometry and topology for physics.
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.I'd say 99.9% of the mathematics you need in physics is geometry ;-).
Topological solitions (defects) and such. https://theconversation.com/the-nob...-to-topology-and-mathematicians-applaud-66532What are some examples where algebraic topology is needed in physics?
Is there any algebraic topology here?Topological solitions (defects) and such. https://theconversation.com/the-nob...-to-topology-and-mathematicians-applaud-66532
Where is the physics?
Where is the physics?
Is there any algebraic topology here?
So, do you think that the title is well chosen?Well, it doesn't say all mathematics. It just says mathematics, and geometry and topology is mathematics.
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.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.
I was asking about the paper you linked to. It seemed like an introduction to algebraic topology, but i didnt see any 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.
I am asking because i would like to see some examples.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 don't know. The article about the Noble prize didnt have much detail.Isn't topological defects and topological charges studied in algebraic topology, or are you suggesting that general topolgy is enough for those applications?
It mentions several physical applications, but do not discuss them in lenght.It seemed like an introduction to algebraic topology, but i didnt see any physics.
I am asking because i would like to see some examples.
I suppose I have to read the article in detail. I must have missed them.It mentions several physical applications, but do not discuss them in lenght.
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?".View attachment 303805
indirectly you classified Yang-Mills and string theory as not physics here.
I did not mean that that article was a source for Yang Mills and string theory but just as source with more examples.But I didn't see them in the article
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.I did not mean that that article was a source for Yang Mills and string theory but just as source with more examples.
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.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.
This would be even more interesting for me to see. Anyone?I guess there are some applications in general relativity as well, but I am not that much into that field
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.Anyway, I thought the thread was about this online "book", not what applications algebraic topolgy has in physics.
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.It is somewhat on topic to ask for some examples, may be from the book itself
https://arxiv.org/abs/gr-qc/9509048v1This would be even more interesting for me to see. Anyone?
Collapse is projection, which is geometryIt 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.
Or algebra?Collapse is projection, which is geometry
So, do you think that the title is well chosen?
That's quite long. Can you pinpoint some of the examples?@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
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?That's quite long. Can you pinpoint some of the examples?
! 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.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?
Many strong force particles get contributions to their mass from classical Yang-Mills solutions weighted by their Chern class. Eta prime is an example.What are some examples where algebraic topology is needed in physics?
in 202323rd of September.
ah yes...Too much work of grading students' work.in 2023
Though the author can postpone the publication to 2030...ah yes...Too much work of grading students' work.
Though the author can postpone the publication to 2030...
It looks like he postponed it again to 2027...The list of errata from the second edition must be worth two entire books I guess!