They're not really point particles like in idealized classical physics, i.e. a single point carrying a mass, charge, etcfxdung said: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?
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.fxdung said: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.fxdung said:Is there any "suggestion" it must be Poincare group?
fxdung said:Please explain at A level
DarMM said: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.PeterDonis said: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
DarMM said: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.PeterDonis said: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.DarMM said: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.
fxdung said: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?
Heikki Tuuri said:In my physics blog
fxdung said: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."fxdung said: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.fxdung said: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.DarMM said: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.DennisN said: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.vanhees71 said: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.vanhees71 said: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 ofA. Neumaier said:It is a stable infraparticle, which means that it has an additional mass degree of freedom, which behaves like an additional momentum dof.
An elementary particle is a fundamental particle that cannot be broken down into smaller components. It is the smallest unit of matter and is believed to be the building block of all matter in the universe.
Scientists have conducted numerous experiments and observations that have shown that elementary particles have no internal structure and behave like point particles. This means that they have no size or shape and are considered to be dimensionless points in space.
One of the main pieces of evidence is the behavior of elementary particles in particle accelerators. When accelerated to high energies, they behave as if they have no internal structure, and their interactions can be accurately described using point particles. Additionally, observations from various experiments, such as scattering experiments, have also shown that elementary particles have no size or shape.
Some theories, such as string theory, propose that elementary particles are not actually point particles but are instead tiny strings that vibrate at different frequencies. However, this is still a topic of debate and has not been proven through experiments.
The Standard Model, which is the current theory that describes the behavior of elementary particles, assumes that they are point particles. This assumption has been very successful in predicting and explaining the behavior of particles in various experiments, further supporting the idea that elementary particles are indeed point particles.