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Is Lorentz group correct?

  1. Jan 15, 2007 #1
    Is Lorentz group correct?, my question is let's be a group A so the Lorentz Groups is a subgroups of it so [tex] A>L [/tex] (L=Lorentz group , G= Galilean group) of course if we had an element tending to 0 so:

    [tex] A(\hbar)\rightarrow L [/tex] (Group contraction)

    so for small h the groups A and L are the same and the laws of physics are invariant under L or A transform, but a pure quantum level when Planck's h is different from 0 the A and L group would be completely different.

    this 'Group contraction' would be an analogue of:

    [tex] L(\beta)\rightarrow G [/tex] where 'beta' is v/c for small velocities we find that law of physics are invariant under Galilean or Lorentz transform.

    the question is what would be the 'A' group?, could we find a group A so contracted in elements b=v/c or e=h gives us the Lorentz or Galiean groups and that the transformations (Lorentz, galilean,..) are linear?.
     
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  3. Jan 15, 2007 #2

    mma

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    It's interesting.

    I think you mean something like this:Einstein and Group Contractions, isn't it?

    I am afraid that I hear the phrase "group contraction" now at the first time, so I know nothing about this, but it seems to me very interesting. I hope that you will find an expert of this topic here; I will read you with pleasure.
     
  4. Jan 15, 2007 #3

    Chris Hillman

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    I am familiar with contraction, but Kevin's post appears too incoherent for me to make out his question.

    A possible reference for the notion of contraction would be Sharpe, Differential Geometry, a textbook on Cartan geometry. This is a notion which arises naturally in Lie theory and which can be used to relate various Lie groups by examining their Lie algebras.
     
  5. Jan 16, 2007 #4

    mma

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    Could you give a web reference for a brief summary of group contraction (perhaps with special regard to Lorentz-group)? I mean something like a Wikipedia article.
     
  6. Jan 16, 2007 #5

    Chris Hillman

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    [screetch]Wikipedia?!!!![/screetch]

    Two seconds with Google yielded this:

    http://eom.springer.de/C/c025850.htm
     
  7. Jan 16, 2007 #6

    robphy

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    And another two seconds yields
    http://www.pnas.org/cgi/reprint/39/6/510
    E. Inönü, E.P. Wigner, "On the contraction of groups and their representations" Proc. Nat. Acad. Sci. USA , 39 (1953) pp. 510–524

    Instead of contraction, a similar term [in the "opposite direction"] used in the literature is "deformation",
    e.g., http://www.numdam.org/numdam-bin/fitem?id=PMIHES_1998__S88__73_0
    Faddeev, Ludvig, "A mathematician's view of the development of physics." Publications Mathématiques de l'IHÉS, S88 (1998), p. 73-79
     
    Last edited: Jan 16, 2007
  8. Jan 16, 2007 #7

    mma

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    Thank you, robphy and Chris!
    Now reading...
     
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