1. Why are there an unfixed number of particles? Texts usually present some hand-waving argument with bits and pieces of SR and NRQM thrown together. Are there more rigorous explanations? 2. How can the scalar fields suddenly be opeartors? I never understood this step mathematically, one moment they are working with the fields in a scalar differential equation, and the next they are somehow opeartors which obey a non-zero commutation relation (something a simple multiplicative scalar operator could not obey) 3. How are particles in QFT defined? Particles in QM and SR were defined by localized lumps of four-momentum travelling through spacetime. How do we even define localization in QFT without a position (or maybe a four-position) operator?