Hi,
My question is about why quantum fields are used.
Are quantum fields just a reinvention of the ether? It seems like something superimposed on spacetime (from which theoretically spacetime should emerge in the case of gravity) from which particles can pop in and out of.
How wrong is...
i'm not a LCQ person, but diffeomorphisms are just differentiable bijective maps, which in physics terms means just coordinate transformations.
lorentz invariance means that the transition function taking you from one coordinate patch to another contains the lorentz group.
diffeomorphisms...
in field theory, depending on the interactions, the size of the lagrangian can be scaled up or down by redefining the fields. if the action/lagrangian is scale invariant, then nothing really changes. however, if it isn't the interaction terms change in size.
in the quantum mechanics case, you...
why does the lagrangian or lagrangian density have to be real?
it's not an observable in general. it's a lorentz scalar and nothing more. it is constructed from observables -- such as the energy and momenta, etc..
you can try to impose it to be real, but then you will get no damping in the...
there is no reason paths have to be differentiable. in fact the stochastic approach to QM gives inherently non-differentiable paths.
a path which is not continuous would mean a particle that starts at some point and disappears into the vacuum an then reappears and then makes it out to some...