Problems on quantum field operators in QFT

  1. Hello!

    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. tom.stoer

    tom.stoer 5,489
    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. Thank you very much!
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