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Problems on quantum field operators in QFT

  1. May 10, 2010 #1

    I met some annoying problems on quantum field operators in QFT.They are as follows:

    (1)The quantum field operator( scalar field operator, for example),is often noted as

    φ(r,t). Can it be interpreted as like this: φ(r,t) is the coordinate represetation of a

    more abstract,theoretical operator φ in Hilbert space?

    (2)Is there exist the represetation(such as momentum, coordinate.....) which is similar to

    that in quantum mechanics in QFT?

    Thanks for reply!!!
  2. jcsd
  3. May 10, 2010 #2


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    Science Advisor

    Regarding 1) no, r is an "index", not an entity living in a Hilbert space. This becomes clear if one derives quantum field theory of a scalar field from infinitly many coupled harmonic oscillators.

    Regarding 2) yes, these are the so-called creation an annihilation operators obtained by Fourier transform of the field operators, usually denoted as [tex]a^\dagger(p)[/tex] and [tex]a(p)[/tex]
  4. May 10, 2010 #3
    Thank you very much!
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