They're not really point particles like in idealized classical physics, i.e. a single point carrying a mass, charge, etcElementary particle can be consider as a "wave packet" of the field,but a "packet" of field must have a size.Why do we know elementary particle is point particle?
Well in Quantum Field Theory a "particle" is simply a space of states that transform into each other under the Poincaré group and other internal symmetry groups. This space must be irreducible, i.e. no subspaces within it transform separately without mixing.Please explain at A level
Well if you are doing it in a Minkowksi background it would be. However the same results essentially apply to QFT in curved space time since most spacetimes are asymptotically flat.Is there any "suggestion" it must be Poincare group?
Moderator's note: Thread level changed to "A".Please explain at A level
I think you mean all spacetimes are locally flat, i.e., the group of local transformations whose irreducible representations define "particles" is still the Poincare group. No curved spacetime has the Poincare group as a global group of transformations, not even if it is asymptotically flat (and I'm not sure I would agree that "most" spacetimes are asymptotically flat anyway, since I don't know how you would define a measure on the set of all possible spacetimes).the same results essentially apply to QFT in curved space time since most spacetimes are asymptotically flat.
It's to do with formulating scattering theory in curved backgrounds, the theory becomes more complex if the spacetime is not asymptotically flat and in most cases the S-matrix is not known to exist. It's a complicated subject I shouldn't have tried to summarize it in one line. The "most" was loose, i.e. "most spacetimes one sees in practice" rather than a formal measure theoretic statement. As you said the set of spacetimes is a poorly understood problem.I think you mean all spacetimes are locally flat, i.e., the group of local transformations whose irreducible representations define "particles" is still the Poincare group. No curved spacetime has the Poincare group as a global group of transformations, not even if it is asymptotically flat
Ah, ok, so for this particular case the relevant group is given by the asymptotic spacetime.It's to do with formulating scattering theory in curved backgrounds
Let me gather the details. I don't have all the theorems and references to mind off the top of my head. I'll do a bit of reading of my old notes and post something detailed.Ah, ok, so for this particular case the relevant group is given by the asymptotic spacetime.
I believe that in spacetimes that are bounded at a fixed time, a conventional S-matrix cannot exist because of the Poincare recurrence theorem.It's to do with formulating scattering theory in curved backgrounds, the theory becomes more complex if the spacetime is not asymptotically flat and in most cases the S-matrix is not known to exist.
Let us use a radio transmitter to send a wave packet containing just one photon of a wavelength 1 meter to space. Suppose that an observer in a rocket approaches us almost at the speed of light. He might measure the photon wavelength as 1 micrometer. He is holding a photographic plate where a very small dot appears.When field is excited then it create a particle. A mode of excited field can consider as a particle (a quantum of field). But in the book QFT of Zee, he say that a particle is a "packet wave" of field. So I do not understand because a "packet wave" is a set of many modes. Is it correct that only when "particle" enters the measure machine it become "packet" (point particle) so when we observe the experiment we see "point particle"? Is that Zee want to say?
Your blog is not a valid source. Please do not reference it here.In my physics blog
Protons and neutrons are composite objects--they are made of three quarks. Electrons and neutrinos, as far as we can tell, are not composite objects.Why do proton, neutron.... have sizes, but electron,neutrino..... are point particles?
My understanding is: when people say that elementary particles, such as electrons, are point particles, they mean that they are described by the Dirac equation / QED with great accuracy. The Nobel prize winner Dehmelt, who established strong experimental limitations on the size of the electron, wrote (Physica Scripta. Vol. T22, 102-110, 1988): "an elementary Dirac particle, such as the electron, is the closest laboratory approximation of a point particle."Elementary particle can be consider as a "wave packet" of the field,but a "packet" of field must have a size.Why do we know elementary particle is point particle?
fxdung said:Why do proton, neutron.... have sizes, but electron,neutrino..... are point particles?
As I said above the electron and neutrino aren't really point particles in any sense in modern quantum field theory.Why do proton, neutron.... have sizes, but electron,neutrino..... are point particles?
This is way beyond my knowledge, but it sounds very interesting, and if you could explain this further I would be very interested. Particularly what "sharp mass" means.Beyond even this, the electron doesn't possess a sharp mass. Nonperturbatively the electron's two point function has no poles. So an electron is in fact sort of an integral over irreps.