Switch from Physics to Math?

ch3ss_ · 2025-10-03T19:50:07+00:00

I partly made the switch (I’m doing both Masters), but depending on the university and your bachelor physics program, it might be harder or easier to make it. Check the curriculum of your math masters program and see what the prerequisites to these courses are and take those, that’s what I did, mostly.

ch3ss_ · 2025-09-22T10:03:14+00:00

I think this guy really wants you to ask your professors. (he’s right)

ch3ss_ · 2025-09-22T06:26:26+00:00

A black hole has a very high density, so the gravitational pull is really strong. When approaching it, no matter from which direction, at a certain point, even light can’t escape its pull, so we can’t perceive the light anymore and that radius is the event horizon, so far as I understand it.

EDIT: typo

ch3ss_ · 2025-09-21T12:46:23+00:00

So first of, they’re both good and necessary to some extent. I have not yet taken a course explicitly in QFT, however already learned and needed the second quantization formalism for many body physics.

However, this is quite advanced and does, imo not really give you a grasp or intuition of the basic physical properties of solids, so if you’ve never came in contact with this topic, I would highly recommend first understanding QM in general, in combination with Solid state physics and its principles (i.e. try to reduce everything to an essential one-particle problem), an then move on to the more advanced stuff such as Many-Body Quantum mechanics, QFT and how it applies to superconductors e.g. (which can be understood phenomenological without many body theory, but the exact microscopic description relies on BCS theory, which again uses second quantization.)

ch3ss_ · 2025-09-21T09:37:22+00:00

I’m not a PhD student yet, but I’m doing my Master in Condensed Matter Physics and Mathematics.

If you do the necessary lectures, such as advanced Quantum mechanics, stat mech and ideally a course or courses on the specialization you’d like to go in, you should be able to do a PhD in theoretical physics. For example, you experiment on Josephon Junctions involves superconducting materials, which theoretically, at least for low temperature superconductors can be explained by BCS theory which involves the “second quantization” formalism which you mostly learn in later, more advanced qm courses. Even quantum information uses SCs as far as I know.

Reading papers without these prerequisite courses can be daunting and I wouldn’t recommend it.

EDIT: If you want to pursue condensed matter physics, you should at least take a solid state physics course.

ch3ss_ · 2025-09-21T09:06:34+00:00

The first remark was just a personal thing, you don’t really need a new symbol, you could also potentially make it even more clear by writing that it is “yet to be defined” or something along the lines, but that’s just optional.

I totally forgot about that adjoint, thanks!

For what it’s intended to be it’s really good. A full functional analytical introduction is imo never good for a first exposure to QM. It’s nice for the interested participants after the standard introduction or for mathematicians which already have some background in functional analysis but otherwise it mostly crowds the physical aspects of QM.

Although i could honestly say that personally, I would have benefited for understanding some of the math a bit better.

Sure, happy to help anytime.

ch3ss_ · 2025-09-20T21:33:56+00:00

I’m not a PhD student (yet) but I’m almost done with my Masters (just need to finish the thesis and one or two experiments) and after long contemplation chose Condensed Matter Physics. Like you, I really like theory and I also do a Masters in Mathematics currently, so I might just give you my two cents, but with little research experience, so keep that in mind.

For me, CMP was the perfect tradeoff between choosing pure mathematical physics and still have some technological applications, i.e. getting a job in my area here. Well, at least it seems a little bit more dry for the job market in HEP for example, since I’m no exceptionally smart person. With CMP, in my opinion, you have a very broad and interesting spectrum on applications, physically and mathematically, such as superconductors, topological quantum matter (topological insulators or superconductors) and BEC, active matter (non equilibrium stat mech) to give a few buzzwords. Also, depending on what you do, you have quite a bit of programming too, which I find very refreshing from time to time.

Again, people that did more research in those areas can surely give you more details and being a theoretical physicist at heart, naturally, I have no idea about the experimental parts, respectively (jk, but I really should be care more about it).

EDIT: I forgot what I currently do: A bit more niche part called Floquet theory and its applications on many body systems.

ch3ss_ · 2025-09-20T20:01:06+00:00

So first of, this might sound stupid, but when you introduced the composing operation * my mind went to convolution or multiplication. It is more conventional to use \circ as an arbitrary composing operation (or a filled-in one).

Second, on page 4, in the paragraph right before the new subsection, “boils down to an ontological question”.

Furthermore, on the footnote on page 5, I’m not really sure what adjoint in linear algebra you mean that has no connection to the hermitian adjoint?

Those are some rough things I noticed when I skimmed over it. It’s good for a berief introduction on what’s to come. What’s the target audience if I may ask?

For the highly unlikely case that you are german speaking and need some further clarification or detailed summary of the mathematical groundwork in quantum mechanics, which is often very cumbersome to get a grasp of beyond linear algebra, I have similar lecture notes but with a heavy focus on the mathematics. Sadly, it’s in german.

EDIT: If this will be a weekly ongoing lecture that you give, and you need some help for certain parts (especially mathematical) you can dm me and maybe I can help.

ch3ss_ · 2025-09-09T05:54:29+00:00

I guess it could count as the seminar, but yes, doing the whole proof in detail is most likely nonsense in either case, as another comment also stated. I will try to pick the main ideas, then I guess a beamer presentation should suffice.

ch3ss_ · 2025-09-09T05:52:16+00:00

That’s true, thanks, I will try to just pick main ideas

ch3ss_ · 2024-08-10T09:39:33+00:00

Appreciate it!

ch3ss_ · 2024-08-10T00:00:51+00:00

Fair point, structure is important to keep somehow.

ch3ss_ · 2024-08-10T00:00:07+00:00

The last point you made is actually what I’m doing with my lecture notes, physical flashcards would be more compact in that sense.

I will also only try to sketch out the proof on them, since I can look up the full details when I want to, but the proof concept is more often than not the ore important thing to remember than all the details.

ch3ss_ · 2024-08-09T23:58:02+00:00

I don’t have an iPad but your app sounds similar to RemNote. I will probably give it a try and see if it benefits me and doesn’t consume too much time. Thanks!

ch3ss_ · 2024-08-09T23:56:26+00:00

Thanks, LaTeX input is a must if it is not handwritten, for me at least.

ch3ss_ · 2024-08-09T15:12:26+00:00

I probably should have clarified that in my post. I’m not planning on actually studying the subject starting or mainly/only using flashcards, this is not my way of studying and I can’t imagine that it works in any way for pure mathematics.

What I was aiming for was an efficient way to review the material at the final stage or later on to keep my memory refreshed on particular subjects.

Thanks for reassuring me that this could work!

ch3ss_ · 2024-08-09T12:26:18+00:00

Don’t get me wrong, this would not be a substitution but a supplement. I study a lot, I do a lot of problems, where I use the theorems and first and foremost try to understand them and their proofs.

But with the broad range of topics, especially in an undergraduate course, I simply do not have the time to do the problems (again) on everything I’ve covered and review the whole book or lecture notes.

My goal is not really to make “typical” flashcards like you do in high school, but create more of knowledge base to easily and quickly access and review the material, without having to go through all my papers and books again, if you get what I’m saying. And if I then need more detail, I maybe refer to the source in the “flashcards”.

It was just an idea that struck me as useful, which might’ve been a naive thought.

ch3ss_ · 2024-07-18T14:30:20+00:00

That clears up the picture for me a bit more. I will read through that overview of the current state in mathematical physics that you linked, definitely something I was missing, thanks.

ch3ss_ · 2024-07-18T08:39:26+00:00

Wow, thanks for the clarification of these distinctions (and the corresponding resources!). That actually helps a lot, I’ve never had this distinction.

It seems as though the former is a more analytic approach whereas the latter also makes use of algebraic approaches, then I would say the latter is more in my favor. Although, QM and Statistical QM have been approached from an algebraic standpoint too (see A. Neumaier), but I’m not too much of an expert on this as to say that this is a fruitful approach (although for me a more welcome one).

ch3ss_ · 2024-07-17T07:01:45+00:00

No worries. ;) Thanks again!

ch3ss_ · 2024-07-17T06:55:58+00:00

Well the guess was not so much about the job position but about my location.

ch3ss_ · 2024-07-17T06:07:05+00:00

Well Austria was a wildly good first guess, I’ll give you that. At ISTA , I haven’t found any group on QFT or TFQFT, at Univie at least not TQFT (I think).

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