I started my studies about quantum field theory but I have some problem to understand the whole concept. I have the following questions:
The Lagrangian contains a dirac term for fermions and a maxwell term for gauge bosons. But does this mean that there is only one dirac field for all fermions? I guess this is not the case but I don't understand why we do not sum over the masses and other quantum numbers in the Lagrangian to distinguish the fields?
We interpret particles as excitations of the field. Should we assume that there is one "field" for each particle or do we create for example three electrons into a common field? But what about the pauli exclusion principle in this case? Is it impossible to have two fermions of the same kind (and same quantum numbers) in the whole universe (the occupation number of fermions is 0 or 1)?