# Problems on quantum field operators in QFT

by Dyson
Tags: field, operators, quantum
 Sci Advisor P: 5,443 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 $$a^\dagger(p)$$ and $$a(p)$$
 Quote by tom.stoer 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 $$a^\dagger(p)$$ and $$a(p)$$