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Direct Product

  1. Mar 10, 2010 #1
    When the direct product is in the exponent of some variable, how is it defined?
     
  2. jcsd
  3. Mar 10, 2010 #2

    haushofer

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    I would say that it's defined via the Taylor expansion. Can you give the explicit expression?
     
  4. Mar 10, 2010 #3
    Like O(3) ^ direct product blah
     
  5. Mar 10, 2010 #4

    haushofer

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    You mean something like

    [itex]

    G^{\otimes}

    [/itex]
    ? I never saw such a thing, but I would then guess it's a notation for

    [itex]
    G \otimes G \otimes G \otimes \ldots \otimes G
    [/itex]

    Does that make sense in your context? Otherwise you should give the exact expression in LaTeX :)
     
  6. Mar 10, 2010 #5

    clem

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    t is defined either by a Taylor expansion or by an eigenfunction expansion.
     
  7. Mar 10, 2010 #6

    George Jones

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    There seems to be confusion in this thread (at least for me).

    Please write down clearly, completely, and precisely what you mean, or give a reference to a text or paper which uses the notation that you want want clarified.
     
  8. Mar 10, 2010 #7
    Something like that. What does it mean?
     
    Last edited by a moderator: Mar 10, 2010
  9. Mar 10, 2010 #8

    George Jones

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    Do you mean "something like" or "exactly like"? You have to be precise.

    Do you mean

    [tex]\overset{k}{\otimes}V?[/tex]

    This is standard notation for

    [tex]V \otimes V \otimes \ldots \otimes V[/tex]

    with [itex]V[/itex] repeated [itex]k[/itex] times.
     
  10. Mar 10, 2010 #9
  11. Mar 10, 2010 #10
    It's the tensor product of N copies of rho.
     
  12. Mar 10, 2010 #11
    thanks
     
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