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What is the use of infinite-dimensional representation of group

  1. Mar 22, 2014 #1
    What is the use of infinite-dimensional representation of lie group?
    Now, I know Hilbert space is infinite-dimensional, and physical states must be in Hilbert space.
    However, for massive fields, the transformation group is SO(3), its unitary representation is finite.
    For massless fields, the transformation group is non-compact ISO(2), but only the finite representation of ISO(2), namely SO(2) representation, has physical meanings.

    I want to know where the infinite-dimensional representation is used in physics?

    thanks
     
  2. jcsd
  3. Mar 22, 2014 #2

    Simon Bridge

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    It provides the most general possible representation of what you are trying to do.
     
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