It' helpful to distinguish between the general structure of a subject and particular examples of it. For example it's entirely possible to have a good and deep understanding of quantum mechanics without having mastered all the details of Laguerre polynomials or selection rules in the dipole...
This is quite wrong, especially regarding Peskin and Schroeder. That book spends half of its chapters working out tedious calculations relating to QED, QCD and standard model phenomenology. Someone who works on some narrow part of string theory, say topological strings or entanglement entropy...
Strong bump dude.
Anyway, point is do math if you enjoy it. Very few people can become Gausses or Eulers, but just be the best you can be. You might not reach greatness, but you'll still have a career that you'll enjoy and you will have contributions you'll be proud of.
How could one go about "preparing" themselves? What is it that all the physicists/mathematicians who transition into finance/wall street usually do to prepare themselves for such a job?
Yeah it's certainly an interesting thread with lots of good insight from an experienced guy. I would be reconsidering theoretical physics as well had I resonated with what he was saying. But in fact, I've greatly enjoyed the journey so far and while I do find parts of physics to be quite boring...
By the way, it's available for free online as a pdf.
The two "subareas" are not really subareas. They aren't really related and there's no real overlap. The main reason is that the tools used in the "physical mathematics" field would be considered "non-rigorous" by the guys working in the...
I would suggest that your first course of action should be to get familiar with path integrals. That's the most widely used tool at the starting stage. It's what Alvaraz Gaume used for the supersymmetric proof of Atiyah-Singer. It's what Witten used to derive the Jones polynomial from...
You're asking many great questions that I've asked myself and researched over the past couple of years regarding what "mathematical physics" is.
Broadly speaking I would divide "mathematical physics" into two categories.
Firstly there's the type of mathematical physics, where you are trying to...
I understand your struggle, and though I'm less experienced than you, I can relate to the feeling of being stuck with learning prereqs. I think the important piece that you are missing, without which everything seems disconnected, boring and hard to remember is "unification". What I mean is that...
If you want a good discussion of the physics AND math behind QM, start reading Shankar. Now. He starts off with a very nice chapter on the relevant mathematics, followed by a chapters on classical mechanics and the experimental basis of QM. Chapter 4 is then a very enlightening read, since he...
I haven't read that book but it should be alright as long as
1. It covers complex analysis, including contour integrals
2. Fourier series and transforms
3. Greens functions
4. Linear algebra, with emphasis on inner product spaces.
Hassani has a pretty decent coverage of these topics...
Learn math, mainly complex analysis and linear algebra by using Hassani. Learn Lagrangian and Hamiltonian mechanics using Landau. Learn Quantum Mechanics using Shankar or Sakurai. Learn special relativity using Schutz. Then you'll be ready for QFT. Enjoy the ride!
For both HET and CMT, classes that are useful and pretty much mandatory to know are graduate level quantum mechanics (Shankar or Sakurai), quantum field theory, and maybe a math methods course. Other useful classes for HET are general relativity, a particle physics/standard model course, and if...
And they'll be discussing QM in a non-calculus based class? What the f*ck man, please tell me I misunderstood something?
Here's the thing man. If you're interested in physics at all, you should be learning it using calculus. For heaven's sake, physics was why calculus was invented in the first...