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fxdung
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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?
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?
Please explain at A level
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
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.
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?
In my physics blog
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 possesses 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.
I am currently gathering all the information required to write this up. It will be a very long set of posts. It was the last thing I promised before going inactive, so I'm working on it.Hi, @DarMM
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.
In QED, the electron mass is a branch point, not a pole, becaiuse of Imfrared effects coming from the zero mass of photons. Thus the electron mass spectrum is continuous.Since when does an electron decay? Within the Standard Model the electron as the lightest charged lepton cannot decay and thus has a sharp mass. It's a stable particle and its Green's function thus has a pole on the real axis of ##s=p_{\mu} p^{\mu}##, which defines its mass.
It is a stable infraparticle, which means that it has an additional mass degree of freedom, which formally behaves like an additional momentum dof - the latter generates the continuous spectrum of the energy. In the QM treatment of multielectronic systems, this dof is generally suppressed. Indeed, infrared problems are not much addressed in the literature.True, but does this imply that the free electron is in fact unstable? If so what's the (theoretical) decay mode, and why isn't this observed?
Here is more on infraparticles. For more on the branch point of the electron propagator, see, e.g., section II ofIt is a stable infraparticle, which means that it has an additional mass degree of freedom, which behaves like an additional momentum dof.