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Lerning the Standard Model and some question about QM

  1. Jun 10, 2007 #1

    I used the last few month two make me familiar with quantum mechanics and read two books. The Feynman lectures on physics and Principles of Quantum Mechanics (R. Shanker).
    I think I have no problems with the bra-ket notation and solving the Schroedinger equation for some simple particle systems. I'm struggeling a bit with QFT however.

    I also have some question which may not be that important
    1)Why does anybody bother about the path integral formalism? I mean in every textbook you read it is more complicated and doesn't give any new insight and so on and even when I understand the idea of the path integral I just can't think of any normal system you can solve by taking a integral over infinite many pathes.
    2)Why do most textbooks spend so much time to solve the problems exactly? I mean not even a hydrogen atom (if you don't take all the approximations like CM etc...) is exactly solvable so would it not be better to spend more time on numerical solutions to the problem or perturbation theory?

    Ultimately I want to do physics with the Standard Model but I see two big problems on the way.
    First of all I did some reading into QFT but even though I can understand the concept I'm not really sure how you can ever apply QFT to a real physical system.
    I also read something about the standard model and I can understand the concept of symmetry groups and the gauge groups and why you need a symmetry breaking to get masses for the W und Z bosons.
    But let's say I have a system with some particles which interact how can I describe such a system and solve it or get a numerical solution.

    So the concrete question: Is is there any book, article or paper you can recommend to learn that?

    thx especially to everyone who read until to this point :-)
    Last edited: Jun 10, 2007
  2. jcsd
  3. Jun 10, 2007 #2


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    The exact solutions are the textbook material per se. They can't be avoided and they're important as they provide the starting point in any pertubative computations. As for the relevance of the path integrals, let's say that without path-integrals there wouldn't have been any Standard Model...
  4. Jun 10, 2007 #3
    If you want to learn how to do particle physics calculations in the Standard Model, then you want to learn, well, basic particle physics. :) There are sort of two paths you can take: a QFT book will teach you how QFT works, why the theory is the way it is, etc., and in the process show you how to do some calculations. A particle physics textbook will aim to teach you how to do calculations right away, without bothering with the (long, complex) derivation of those calculational schemes. It will also teach you the basics about particles which are helpful to know when dealing with them.

    A very good QFT textbook is Peskin & Schroeder, An Intro to QFT.

    A good particle physics textbook is Halzen & Martin, Quarks and Leptons. Griffiths' Particle Physics is popular, and pitched at a little more basic level.

    The path-integral formulation is theoretically very elegant and gives us insight into the structure of field theory. More practically, there are serious complications that arise with canonical quantization of gauge theories. The path-integral formulation avoids these.
    <shrug> Most textbooks I know only do a few very simple problems exactly. And before you can do perturbation theory, you need an exact solution to the unperturbed system. :)
  5. Jun 10, 2007 #4

    thx you both for your answers and I will take a look at the books you have

  6. Jun 28, 2007 #5
    The path integral is useful for visualizing, setting up and organizing a perturbative calculation. That's what feynman diagrams are, just perturbative calculation of some path integral that gives very useful approximate answers.
  7. Jun 29, 2007 #6


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    One of the advantages of the path-integral approach is that the formalism looks more relativistic covariant and gauge invariant.

    Concerning the exact textbook solutions, my opinion is that it is good to know that they exist, but that it is not necessary to study them in detail, unless you really need them in some practical problem.
  8. Jun 29, 2007 #7
    Furthermore path-integral is useful in mathematic problems, however it rised from physical concepts.
    refer to:
    Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Evaluation of Functions by Path Integration." §5.14 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 201-204, 1992.

    Mr Beh
  9. Jun 29, 2007 #8


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    We forgot to mention the most important utility of the path-integral formulation: This is the most useful formulation for treating NON-perturbative aspects of QFT. The best example is lattice QCD, which is entirely based on path integrals. Another example is quantum contributions of instantons.
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