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A Diffeomorphism invariance and gauge invariance

  1. Apr 16, 2017 #1
    Consider the following paragraph taken from page 15 of Thomas Hartman's lecture notes (http://www.hartmanhep.net/topics2015/) on Quantum Gravity:

    In gravity, local diffeomorphisms are gauge symmetries. They are redundancies. This means that local correlation functions like ##\langle O_{1}(x_{1})\dots O_{n}(x_{n})\rangle## are not gauge invariant, and so they are not physical observables. On the other hand, diffeomorphisms that reach infinity (like, say, a global translation) are physical symmetries - taking states in the Hilbert space to different states in the Hilbert space - so we get a physical observable by taking the insertion points to infinity. This defines the S-matrix, so it is
    sometimes said that ``The S-matrix is the only observable in quantum gravity.''


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    1. Why does the fact that local diffeomorphisms are gauge symmetries mean that local correlation functions like ##\langle O_{1}(x_{1})\dots O_{n}(x_{n})\rangle## are not gauge invariant?

    2. Why do diffeomorphisms that reach infinity become global symmetries?
     
  2. jcsd
  3. Apr 16, 2017 #2

    haushofer

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    To answer your first question: diff.invariance enforces the correlators to be constant, see e.g. Zee's Einstein Gravity... book.
     
  4. Apr 16, 2017 #3

    haushofer

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    For your second question: have you read page 90?
     
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