Question

Mathematical physicists, how did you obtain the necessary physics knowledge?

Answer 1

I don’t know, I just throw a bunch of questions at my advisor, go to seminars, look at some physics papers, cry rinse and repeat. It seems to be working so far. There’s no way I’d understand the papers without having attended a seminar talk or something similar related to the specific paper.

I also did some (very basic) physic in my undergrad, but I am not sure that is helping in the slightest tbh.

Answer 2

During my career, I wrote papers about quantum field theories. I do have a vague idea about what quantum field theories are as mathematical objects, but I have absolutely no clue about their physical meaning. I don’t even know the bases of quantum mechanics.

The trick is that you often don’t need to know any physics to work with the mathematical objects relevant in mathematical physics, and you can learn the “physical interpretation” either by osmosis, or studying the physics bit by bit for what you need in the particular project you are working on.

Answer 3

You don't have to speedrun all of physics, you just need to speedrun the specific subfields that are relevant to your research. And depending on the field, you might not even have to finish speedrunning those; just understanding the recent papers and their related work sections can be enough to come up with a new idea (or at least understand one that's given to you by an advisor...)

Answer 4

In my experience a good amount of “mathematical physics” is just mathematics with some (possibly vague) physical motivation.

I got a paper in a math journal with word “physics” in it’s name just by having a Poisson bracket in the paper. This is a Lie bracket with some extra conditions which can be used in Hamiltonian mechanics.

Answer 5

I may be more of a peculiar case because I actually come from a physics background initially before I started working more towards theoretical physics/mathematical physics/math after going back and formally studying math. Nevertheless, I don’t think that makes my opinion completely obsolete so here goes.

Firstly, it may *seem* like some pure math students are able to quickly pick up necessary physics knowledge, but the reality is that they don’t, it’s fairly specific subfield knowledge and the minimum they need to know to function. It’s not as daunting of a task as obtaining a physicists’ knowledge of physics in a fraction of the time, just a lot of bits and pieces.

Secondly, a significant part of mathematical physics is just mathematics and the physics emphasis required isn’t problematically deep in many cases. This does depend on the subfield of mathematical physics and the type of research you are doing, but it is a general principle.

Essentially, if you’re a mathematician, it’s often not that incredibly large of a jump to bridge over to some field in mathematical physics, since you’ll find yourself at home with the nature of the subject.

Answer 6

Mathematical physicists often don't know very much physics. While there are certainly exceptions, a lot of work in that field does not address questions which are of interest to most physicists. Some of this is just because of differing preferences for mathematical rigor, but more importantly, discussions in mathematical physics tend to be physically superficial. This is presumably because the physical analog of mathematical maturity isn't easy to pick up on the side.

If you're interested in the mathematics more than the physics, this shouldn't be a problem. You just learn up some motivating words and then treat whatever system you've imported from physics as a purely-mathematical one, asking whichever questions appear to you to be mathematically interesting.

Answer 7

I think there's always some compromise. I work in mathematical physics on my PhD, but I majored in Physics. As such, the mathematics side is a bit lacking (compared to someone who majored in maths, anyway), and I for sure won't speed run all the basic maths while in the PhD, just the necessary parts and let physical intuition be my guide.

 The same thing happens for someone who majored in math, they try to learn the physics that is indispensable for the problem they are working and then focus on their strong side: they have a understanding and familiarity with the mathematical objects describing that theory that your average physicist doesn't have.

On the long term, I'll end up studying the basic math that I left behind and the mathematician will study more physics as well, so both cases get well informed about both areas further into their careers, its not something you need to have accomplished by the time you finish your phd.

Answer 8

I took a graduate level quantum mechanics course within the physics department while being a math PhD. I also took a topics course my advisor taught on quantum field theory and read a couple textbooks my advisor recommended. It definitely helped that I had a background in physics in undergrad but the basics of quantum mechanics are honestly very similar to linear algebra, just in a different notation.

Answer 9

(when it comes to the whole QFT, Strings, Loops, ... side of the physics world)

Don't be afraid to read popular treatments about the subject! It will get you used to the Lingo. A great ressource are Leonard Susskind's Theoretical Minimum Lectures on Youtube.

But most importantly, read "Geometry, Topology and Physics" by Nakahara once you have the basics down. It will help you make the connection between math and theoretical physics.

Answer 10

My uni actually offers a mathematical physics degree which is pretty much just have math half physics. (Ik it wasn't quite what your asking sorry).