The discussion revolves around the interpretation of the field function Φ in Quantum Field Theory (QFT), focusing on its role as an operator in the context of second quantization, the absence of a wave function representation, and the implications for statistical interpretations akin to those in quantum mechanics (QM).
Participants do not reach a consensus on the interpretation of the field function Φ or the applicability of statistical interpretations in QFT. Multiple competing views and uncertainties remain regarding the nature of wave functionals and their implications for Lorentz covariance.
Some limitations are noted, such as the dependence on definitions of wave functionals and the unresolved nature of certain mathematical steps in the discussion of Lorentz covariance and multifingered time.
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?