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What is Ad in a proof?

  1. Jun 29, 2010 #1
    I'm reading QFT: Basics in Mathematics and Physics, by Eberhard Zeidler. Once in a while, in his proofs, I see the word (abbreviation?) Ad. For instance on page 375. The author is German and I suppose this imight be common practice in German texts. Does anyone here know what it means?
     
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  3. Jun 29, 2010 #2

    HallsofIvy

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    Since you don't give an example and most people will not have that book available, I think many will be able to answer this. Since this is posted under "Quantum Physics", and linear operators are often used there, without any more information I would suspect something line "adjoint" as in "ad T" is the adjoint of the operator T. Was "ad" used with an operator or just as a word on its own?
     
  4. Jun 29, 2010 #3
    I've seen it used as the prefix for an enumeration of the steps in a proof, but don't know what it stands for. I doubt it's mathematically significant, though I suppose it could also be used to refer back to an enumerated step.
     
  5. Jun 29, 2010 #4
    I'm sorry, I didn't realize that there were some people that don't have a copy of the book. It must stand for some kind of enumeration like case N, case R, etc. That's how it is used on page 375.

    The form is like this:

    Theorem:
    (i) a = b
    (ii) b = c
    Proof.
    Ad (i) ...
    Ad (ii) ...
     
  6. Jun 29, 2010 #5
    It's an abbreviation for "Ad hoc" which means "for this" (case) as you guessed.
     
  7. Jun 29, 2010 #6
    Thanks unusualname.
     
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