Algebra and Physics

>even physicists can't handle elementary mathematical ideas
and this is why science is dying, how do you even get this far without realizing the importance of math?

Group theory is a rather useful tool if you are going to do any sort of theory work. If you are an experimentalist, you can probably get away with only a glancing knowledge so that you can pretend to understand the theorists.

>>8427618
I don't imply it is difficult. The thing is, this is abstract, and physics is practical. My question is very humble, could any physicist tell me when does algebra become relevant? I mean abstract algebra, not stuff like matrices stuff. Is it usefull to know the properties of an abelian group for a physicist? I know that it could become relevant when talking about vector space, which leads to matrices, which is usefull for physicists. But all the abstract stuff is useless right?

>>8427618
>implying he has gotten far
>implying he has learned any of this math
>implying he's not a shitposting freshman despite him asking a freshman level question

good job

>>8427610
Mathematical physics is more of a math field than a physics field imo. Abstract algebra never becomes really useful in physics on its own beyond some specific tool used in QFT. It's a different discipline.

>>8427627
Graph theory is useful to everyone, but it's not algebra.

>>8427610
Particle physics, good luck going through QFT and the Standard Model without Lie groups under your belt.

>>8427610
https://en.wikipedia.org/wiki/Lorentz_group
https://en.wikipedia.org/wiki/Poincar%C3%A9_group

(I'm not a physicist)

>>8427761
But again that requires you only to study those specific algebraic structures, not algebra as a discipline on its own.

>>8427610
Wew lad are you serious?
https://en.wikipedia.org/wiki/Noether's_theorem

>>8427637
all of that is a branch of algebra tho.

say you are interested in an infinite dimensional vector space, which is common (e.g. you want to do something fourier-y and you want a linear subspace for every frequency on a continuum). or say that you want your basis elements to be things like th collection of all analytic functions from R to itself.

well matrices aren't going to cut it exactly. yes, you can invent notation for the infinite versions, but you want to make sure that they still have the right properties. what properties? well, the ones axiomatized in the abstract theory of vector spaces.

why do we consider things which can be scaled by R or C or Q vector spaces, but not Z? well because only the first form fields while the latter doesn't, and you use abstract properties of fields to prove things like the existence of bases. (incidentally modules - linear combinations of some additive structure scaled over a ring - do not have to have bases). you are already assuming a lot of stuff abstract algebra had to build up.

also, groups should be reason enough. they describe symmetries, and help reveal properties occluded by coordinates.

>>8429190
Biggest retard in this thread and possibly on this website.

>>8430010
What? Explain yourself, please.

>>8429184
Then you'll struggle to understand the concepts unless you pick it up yourself. Most physicists learn their mathematics outside the classroom. I don't agree that's a good way of doing it, but you can only have so many credits in a degree.

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>>8428451
https://en.wikipedia.org/wiki/Particle_physics_and_representation_theory

I'm sure hard math is everywhere. It's more a matter of how much the people working on a field comprehend and thus use. Look at this shit
https://en.wikipedia.org/wiki/Standard_RAID_levels#RAID_6

>>8429184
If you want to be the one creating new stuff, you better not only look at the things that are already there and used in physics.

>>8427610

well you got your projectile motion parabolas...

those are algebra

Gauge Theory is the obvious answer, but at more fundamental level just quantization in general is an algebraic procedure. i.e. Formally done via deformations of commutative algebras into noncommutative algebras.

>>8427610
>When does English become useful for a writer? I don't see any use in learning vocabulary and other useless stuff.

This is you.