- #1

Ringo Hendrix

- 9

- 3

Ok. Very long post incoming. I'm kind of in a conundrum where my context is important. I am self-teaching theoretical physics slowly but surely. My end goal is to be able to mathematically comprehend various quantum gravity theories such as LQG and String Theory. My calculus roots go back to 2014 and I learned some major things in physics conceptually but only mid 2021 did I really start formally teaching myself. Started with Leonard Susskind's lectures, and Khan Academy for vector calculus. Improved my intuition of classical mechanics with various texts including David Tong's notes, from orbits to Noether's theorem and Liouville's theorem. Got some Special Relativity intuition there as well but more a refresher of things I learned from 2014-2021. Then, I tackled linear algebra and undergrad quantum mechanics via Griffiths- that went pretty well for almost a year. While the text clearly wants me to just go along with formulae, I truly like to understand everything I'm doing as fully as I can and be able to derive things. So when I got to Chapter 8 with Airy functions it led me on a path to want to study complex analysis... and improve and expand my knowledge of special functions, PDEs, vector calculus, linear algebra, etc etc etc.

So that took me to 2023 where I spent much of my time 'thoroughly skimming' Riley's Mathematical Methods text, more so for intuition rather than full understanding. It has greatly helped enhance my intuition of pretty much everything, from series to Sturm-Liouville theorem to the aforementioned topics that set me on this journey. Late last year I actually started with Griffiths EM while hitting a low point with Riley's math methods but it eventually led me right back to Riley for PDE topics such as Dirichlet boundary conditions. (I supplemented with Tong's notes when confusion arose) I've finally clawed my way up to complex analysis and have been supplementing with Faculty of Khan's extremely helpful series of videos on the matter.

Now I don't know which path to take. Also, I am quite familiar with Susan Rigetti's "so you want to learn physics?" site, it's been somewhat helpful.I sincerely want to resume QM, this time in full with solving way more problems- I feel with my enhanced intuition I could fly through Griffiths (compared to last time) but it is undergrad level and doesn't discuss path integrals, density matrices, etc. Sakurai or Shankar don't seem like convincing routes based on reviews... I'd be better to go graduate from the start but don't know a suitable text.

Besides, before I'm ready for that, it would do me wonders to study thermodynamics/statistical mechanics (for from-scratch knowledge building of subjects like blackbody radiation- I have a copy of Schroeder maybe I could time my studies where its quantum chapter overlaps with Griffiths' statistical chapter?) It's obviously immensely important for my end goal. Will probably need to tackle graduate level.

And of course electromagnetism- but I don't particularly want to go too in depth with it since the EM I intend to study is the quantum field theory and I suspect it can be studied fairly independently- perhaps Tong's notes will suffice? They seem to the point. Polarization and waves seem useful concepts to learn more about- particularly when I get to gravitational waves.

I can't stress enough how eager I am to start GR and differential geometry. I've considered running through Carrol's Spacetime and Geometry since you don't seem to need background knowledge on topology.

In Riley, I'm about on to the Tensors chapter- and Group Theory which I am hyped for.

Through this disjointed experience I'm seeing how all these different topics are intertwined.... That said- I'm beyond itching to study differential geometry. I know for my end goal, I'll need a much more formal approach to mathematics. Like I need Set Theory for topology (don't I?) and I am deeply interested in mathematical/abstract logic... more advanced complex analysis, real analysis, group theory etc for my end goal. Do I start with basics then re-do it all over again formalizing it or just learn the more formal approach first and be done with it?

Now, I don't know if I should resume Riley for Tensors and Group theory or move on entirely- is there a text which better starts from scratch all of this more abstract math? Arfken might be a good place to start? Zill also discusses sets, I believe, but doesn't go past complex analysis. But I like his descriptions.

Sorry, I know this is a very, very long post- I'm clearly lost in the woods but I just am deeply passionate about physics and want nothing more than to be able to get to the level I'm wanting... without having months-long blocks like I've been having. Am I doing better than I think and being hard on myself? Any advice is greatly appreciated.

Bonus- me deriving Pauli spin matrices and Schwarzschild solution.

So that took me to 2023 where I spent much of my time 'thoroughly skimming' Riley's Mathematical Methods text, more so for intuition rather than full understanding. It has greatly helped enhance my intuition of pretty much everything, from series to Sturm-Liouville theorem to the aforementioned topics that set me on this journey. Late last year I actually started with Griffiths EM while hitting a low point with Riley's math methods but it eventually led me right back to Riley for PDE topics such as Dirichlet boundary conditions. (I supplemented with Tong's notes when confusion arose) I've finally clawed my way up to complex analysis and have been supplementing with Faculty of Khan's extremely helpful series of videos on the matter.

Now I don't know which path to take. Also, I am quite familiar with Susan Rigetti's "so you want to learn physics?" site, it's been somewhat helpful.I sincerely want to resume QM, this time in full with solving way more problems- I feel with my enhanced intuition I could fly through Griffiths (compared to last time) but it is undergrad level and doesn't discuss path integrals, density matrices, etc. Sakurai or Shankar don't seem like convincing routes based on reviews... I'd be better to go graduate from the start but don't know a suitable text.

Besides, before I'm ready for that, it would do me wonders to study thermodynamics/statistical mechanics (for from-scratch knowledge building of subjects like blackbody radiation- I have a copy of Schroeder maybe I could time my studies where its quantum chapter overlaps with Griffiths' statistical chapter?) It's obviously immensely important for my end goal. Will probably need to tackle graduate level.

And of course electromagnetism- but I don't particularly want to go too in depth with it since the EM I intend to study is the quantum field theory and I suspect it can be studied fairly independently- perhaps Tong's notes will suffice? They seem to the point. Polarization and waves seem useful concepts to learn more about- particularly when I get to gravitational waves.

I can't stress enough how eager I am to start GR and differential geometry. I've considered running through Carrol's Spacetime and Geometry since you don't seem to need background knowledge on topology.

In Riley, I'm about on to the Tensors chapter- and Group Theory which I am hyped for.

Through this disjointed experience I'm seeing how all these different topics are intertwined.... That said- I'm beyond itching to study differential geometry. I know for my end goal, I'll need a much more formal approach to mathematics. Like I need Set Theory for topology (don't I?) and I am deeply interested in mathematical/abstract logic... more advanced complex analysis, real analysis, group theory etc for my end goal. Do I start with basics then re-do it all over again formalizing it or just learn the more formal approach first and be done with it?

Now, I don't know if I should resume Riley for Tensors and Group theory or move on entirely- is there a text which better starts from scratch all of this more abstract math? Arfken might be a good place to start? Zill also discusses sets, I believe, but doesn't go past complex analysis. But I like his descriptions.

Sorry, I know this is a very, very long post- I'm clearly lost in the woods but I just am deeply passionate about physics and want nothing more than to be able to get to the level I'm wanting... without having months-long blocks like I've been having. Am I doing better than I think and being hard on myself? Any advice is greatly appreciated.

Bonus- me deriving Pauli spin matrices and Schwarzschild solution.

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