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Mathematics for QFT

  1. Jun 26, 2012 #1
    Hello,

    I am trying to find out (searching did not return anything useful) what kind of mathematical background one needs to understand QFT comfortably (if such state can ever be attained :D). By comfortably I mean being able to concentrate almost entirely on the physics part rather than pick up math at the same time. Specifically, I mean not only the bare prerequisites to understand the material, but also, the mathematical topics which might be a bit off the main track but prove useful nonetheless.

    To provide an example, after taking a first semester undergraduate quantum, I think that a solid preparation for QM would involve Linear algebra, Fourier analysis, and ODE. I am looking for similar ideas regarding QFT.
     
    Last edited: Jun 26, 2012
  2. jcsd
  3. Jun 26, 2012 #2
    Hm, I don't know enough about QFT to help, but I think your specification "Specifically, I mean not only the bare prerequisites to understand the material, but also, the mathematical topics which might be a bit off the main track but prove useful nonetheless." is going to be too strict for your liking, since when I apply it to the case of quantum mechanics, I would definitely include group theory, Hilbert spaces, and quite likely some functional analysis (and maybe even some other things that I'm forgetting atm).
     
  4. Jun 26, 2012 #3

    nicksauce

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    So some things to do

    -Basic relativity/tensor analysis: Be able to understand and manipulate expressions written in Einstein summation notation, be able to write down Maxwell's equations covariantly

    -Fourier analysis

    -You be familiar with classical field theory (i.e., going from the Lagrangian/Hamiltonian to the equations of motion, and knowing Noether's theorem)

    -Complex analysis - you might run into the occasional integral that must be evaluated with techniques from complex analysis

    -Some group theory might be helpful - You'll probably run into terms like "Representation of the Lorentz group"

    That's all I can think of right now
     
  5. Jun 27, 2012 #4
    Very good :) Could you tell me what is a typical background for group theory? I hear it come up on this forum quite often.
     
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