- #1

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- #1

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- #2

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you need more math.

- #3

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Classical Mechanics (especially Lagrangians)

Electromagnetism

Statistical Mechanics (Can get away without knowing, but it helps on occasion)

Quantum Mechanics (Need to know VERY well)

As well as some others, but you can make due with those four, although it will not be easy. Math-wise however, I would say at minimum (and I stress AT MINIMUM):

Calc

ODE's

Linear Algebra

PDE's (Very important)

Group Theory

Basic topology

- #4

Science Advisor

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(Applied or pure) complex analysis; basic special relativity.

- #5

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If you are self studying, you are probably ok to start. Just make sure you use an accessible book to learn from (I hear good things about Mandl and Shaw). If you are considering taking a class, you should talk to the professor, since only he knows what he expects from his students.

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- #7

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Also, topology is really only important if you want to learn functional analysis and delve into algebraic QFT. It isn't necessary at all for an introduction.

- #8

Gold Member

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You can certainly get by without pure complex analysis or without any group theory. You definitely don't need to know Lie Algebra. You needn't have even heard of topology.

I think if you understand E&M and Quantum Mechanics at the level you claim (you should be comfortable with the path integral formulation of quantum mechanics too) you can learn a lot of QFT if you choose the right level book. I would look at A. Zee's book or Klauber's book.

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- #10

Science Advisor

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- #11

Homework Helper

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- #12

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Vector Calculus, Complex Analysis, Optimization. good to know.

- #13

Science Advisor

Education Advisor

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- #14

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You may need contour integral, Lagrange/Hamiltonian formulation of mechanics, classical electrodynamics especially specially relativity and the covariant formulation of Maxwell eqns, and a bit Lie group/algebra

Unless you are really interested in mathematician's QFT, e.g. Quantum Field Theory by Gerald B. Folland, real analysis should not be necessary...

Have a look at Mark Srednicki's quantum field theory, check what kind of background is needed

Unless you are really interested in mathematician's QFT, e.g. Quantum Field Theory by Gerald B. Folland, real analysis should not be necessary...

Have a look at Mark Srednicki's quantum field theory, check what kind of background is needed

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- #15

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The only major missing piece in your first post list was Lagrangian mechanics, but the basic formalism can be understood quickly by a good student.

- #16

Gold Member

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Notice how neither graduate nor undergraduate physics departments require students to study real analysis, differential geometry, abstract algebra, or topology (from what I know). Taking any of these courses is not a horrible idea, but it is important to recognize that the math department has a very different culture and purpose for the study of these subjects than physics, and you can probably get by simply learning what you need on your own rather than going through any of these courses (none of which are even remotely trivial).

As a physics graduate student doing fairly mathematical Condensed Matter Theory, I WHOLLY agree with the above statements.

I double majored in mathematics and physics as an undergraduate. I took plenty of pure math as well as applied. I am certain nearly all of my time doing pure mathematics would have been better spent learning additional computer science and taking more courses in experimental methods of physics.

- #17

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I often suspect the math department is a bit of a rogue department. Much of what they learn in the purest of pure math courses never seems to percolate down to other fields; even the most esoteric physics (save for string theory) is at least useful to experimenters. L'Hospitals rule was invented long before it was proven to work, which raises doubts about whether the machinery of say, analysis, is merely a titanic linguistic rigamarole or truly a useful invention. Indeed, I heard from one theorist that he found the ways of thinking about series he learned in analysis to be damaging to his understanding of field theory, because you simply cannot take the mathematician's point of view in advanced physics. If you want to find out if a person is a mathematician at heart, show him how renormalization works, and see if he or she has a seizure. It is fascinating how much useful mathematics was invented by applied mathematicians and physicists; the fear, loathing, and disdain for application in the "pure" math department is somewhat reprehensible.

/rant

Also, in my undergraduate research I was dragged kicking and screaming into the world of programming, and discovered that I loved it; I think certain CS courses, especially practicums and low level "how to program" courses could be incredibly handy.

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- #19

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The only major missing piece in your first post list was Lagrangian mechanics, but the basic formalism can be understood quickly by a good student.

Well, I am self-studying the material; I'm not taking any courses...

Also, I didn't mention Lagrangian and Hamiltonian mechanics because I thought it was obvious since one cannot go to a good book in quantum mechanics without knowing the Hamiltonian and Lagrangian formalisms.

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