The discussion explores the relationship between Quantum Mechanics (QM) and Quantum Field Theory (QFT), examining whether QM is a subset of QFT, the differences in their formulations, and the implications of second quantization. The scope includes theoretical considerations and conceptual clarifications.
Participants express differing views on whether QM is a subset of QFT, with some asserting a fundamental distinction and others suggesting a deeper connection. The discussion remains unresolved regarding the equivalence of second quantization in QM and its implications for understanding the relationship between QM and QFT.
Participants note limitations in the traditional teaching of QM versus QFT, questioning why QM is often presented separately despite potential connections through second quantization.
meopemuk said:Strictly speaking, QFT is about variable number of particles.
No. A quantum field theory is primarily about fields, as the name says. Particles appear in general only as approximate asymptotic concepts.meopemuk said:Strictly speaking, QFT is about variable number of particles.
The particle number operator cannot be renormalized in the standard perturbation scheme. To get finite results one needs to renormalize, and to get approximate lifetimes, one needs to sum infinite number of renormalized diagrams - which is neither fixed order perturbation theory nor doable in Fock space.meopemuk said:As far as I understand, the "perturbative/nonperturbative" refers to the method chosen to calculate the S-matrix (including the lifetime of positronium). If you are lucky, you can do that without using the perturbation series, but in most cases it is easier to use the perturbative approach. The chosen calculation method should not have any effect on the (Fock) structure of the Hilbert space. The Fock space structure simply tells you that numbers of particles are good quantum-mechanical observables that commute with each other. So, each Fock sector is a common eigenspace of all particle number operators in the theory.
A. Neumaier said:The particle number operator cannot be renormalized in the standard perturbation scheme. To get finite results one needs to renormalize, and to get approximate lifetimes, one needs to sum infinite number of renormalized diagrams - which is neither fixed order perturbation theory nor doable in Fock space.
Because unrenormalized operators have no meaning in the renormalized theory - all expectations containing it are ill-defined.meopemuk said:Why would we want to renormalize the particle number operator?
Positronium is an unstable composite particle which has a finite lifetime computable by QED.meopemuk said:Besides, in QED we are dealing with stable particles - photons, electrons, protons. What the "lifetimes" have to do with them?