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I State of a representation

  1. Aug 16, 2016 #1
    Hello! I am reading something about representation theory (just started) and I encountered this: "We will denote the state in the adjoint representation corresponding to an arbitrary generator ## X_a ## as |## X_a ##>". What is the state of a generator in a certain representation?
    Thank you!
     
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  3. Aug 17, 2016 #2

    Simon Bridge

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    They did not talk about the state of a generator.
    You have a generator... this can generate a state. They are introducing a notation to help talk about that.
    Maybe you need to go back to find the definitions of "state" and "generator", and find out what a generator does?
     
  4. Aug 17, 2016 #3
    Thank you for your answer. I am still a bit confused. From what I understood generators are part of the Lie Algebra and they can generate the whole Lie Group. For example for SO(2) if S is the generator any rotation by ##\alpha## degrees is written as ##e^{i\alpha S}##. So, I understand a generator generates a whole group which usually acts on a vector space. Please let me know if anything I said is wrong. Now, I just don't understand where the idea of state appears in this as I thought that generators are generating a group not states.
     
  5. Aug 19, 2016 #4

    Simon Bridge

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    I get confusded too and authors can use the same word to refer to slightly different things.
    I do not have the context of the passage - but I would see the above as meaning that |A> is a single state belonging to the group that is generated by A.
    The passages that follow should include examples that will make the matter clear. If they do not, then get a different book.
     
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