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Nonstandard analysis in physics

  1. May 28, 2005 #1

    quasar987

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    Here's what mathworld has to say on nonstandard analysis:

    "Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are less than 1/2, 1/3, 1/4, 1/5, ..., but greater than 0. Abraham Robinson developed nonstandard analysis in the 1960s. The theory has since been investigated for its own sake and has been applied in areas such as Banach spaces, differential equations, probability theory, mathematical economics, and mathematical physics. [...]"

    Does anyone know what the applications to mathematical physics are?
     
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  3. May 28, 2005 #2

    Integral

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    To the best of my knowledge,None, at this point in time. There was also a time when physics had no need for matrix theory and Riemann geometry, so things can change.
     
  4. May 28, 2005 #3

    Hurkyl

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    Well, everything that can be done with Nonstandard Analysis can be done with standard analysis, so you can't prove new things...

    the general assertion is that NSA is more intuitive, and proofs using it are shorter and clearer.

    I believe for physics, the hope is that the description of things with infinitessimals will be clearer than the way they are now. Especially since infinitessimals are already used in heuristic reasoning -- the translation to rigor should be easier.
     
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