The field function Φ in Quantum Field Theory (QFT) is interpreted as an operator in the context of second quantization, where the traditional wave function representation is not applicable due to the non-fixed number of particles. The discussion emphasizes that the Born Statistical Interpretation, relevant in Quantum Mechanics (QM), does not extend to QFT, as it relies on wave functions. Instead, QFT utilizes field operators that create and annihilate particles, adhering to specific commutation relations. The wave functional Ψ, defined on the classical configuration space, serves as a counterpart to the wave function but lacks Lorentz covariance, complicating its interpretation.
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tom.stoer said:OK, I see. You are right, interpreting this expression in QM it corresponds to a density (like a charge density) in space.
I would never call this density a "density operator" b/c a density operator is already defined in non-rel. QM and its meaning is something totally different
mpv_plate said:When reading about the basics of QFT I found there is a so called "density operator" which gives the particle density at a given location. It is the combination of annihilation and creation operator in the position space.
Can the density operator be understood as another possible answer? It basically tells where the particles are in the space. When I use the scattering theory it seems I get similar answer: where the particles go (spatially) after they interact (if I understand that correctly). Is the density operator used in the scattering theory?