Elementary particles,0-Dimensional?

[ShayanJ]

Is there any experimental verification for the fact that elementary particles are point like and have no extension in space or its just an assumption?
thanks

 

[Wrothamis]

Just as assumption, this is why they suffer so many infinity problems. In fact, in string theory they try to smear the point by covering it up with bigger minimum size object called strings.

 

[tom.stoer]

It is misleading to talk of "expansion" or "dimension" of fundamental particles in QFT. There are certain attributes that are similar to 0-dim. particles in classical field theory, but there are also other quantities that cannot be interpreted based on point particles; fundamentally there are no point particles in second-quantized QFT. This picture regarding QFT ans string theory is inspired by drawing Feynman diagrams where in qFT particles meet at vertices. But both the vertex and the whole Feynman diagram stuff is a mathematical concept valid in perturbation theory which is not able to cover the full parameter space of the theory.

When talking about experimental indications regarding pointlike particles one typically means that at a certain energy there are no signals of a substructure. But one does not "see" these particles directly.

 

[torquil]

It is misleading to talk of "expansion" or "dimension" of fundamental particles in QFT. There are certain attributes that are similar to 0-dim. particles in classical field theory, but there are also other quantities that cannot be interpreted based on point particles; fundamentally there are no point particles in second-quantized QFT. This picture regarding QFT ans string theory is inspired by drawing Feynman diagrams where in qFT particles meet at vertices. But both the vertex and the whole Feynman diagram stuff is a mathematical concept valid in perturbation theory which is not able to cover the full parameter space of the theory.

Isn't the following the case:

In ordinary QFT theories, the Fock space is spanned by finite products of one-particle point states (corresponding to Dirac delta distributions). Thus one can say that such QFT involves point particle states.

On the other hand, in a space-time formulation (not world-sheet) of the hypothetical string theory (i.e. "String Field Theory"), the Fock space would not be spanned by such states. Its Fock space would be spanned by something like finite outer products of e.g. closed curve states. I.e. the basic state would not correspond to a point, but a curve.

 

[tom.stoer]

The Fock space is spanned by states created via creation operators. There are no pointlike particles. Comparing the Fock space of an ordinary QFT and at the Fock space of a quantized string there is not so much difference.

Why do you say "one-particle point states (corresponding to Dirac delta distributions).", why not simply "one-particle states"?

 

[torquil]

The Fock space is spanned by states created via creation operators.

Yes, that is one choice of basis, and the one that is almost always chosen. This is sensible, since this method takes advantage of the spacetime translation symmetry for purposes of mathematical simplification and elegance.

It is, however, not necessary to use this momentum eigenstate basis. In principle, for ordinary QFT, one could use a position eigenstate basis where the creation operator generates a point state, without a definite particle number. It would not look as nice since one would not take advantage of the nice translation symmetry of spacetime.

It is evident from the path-integral formulation of an ordinary QFT that initial and final states in an amplitude can be chosen as point states.

Comparing the Fock space of an ordinary QFT and at the Fock space of a quantized string there is not so much difference.

My comment was regarding second quantized string field theory, not the string worldsheet field theory. As I understand it, creation operators in a string field theory will be completely different. One such creation operator would be accompanied by not only a few quantum numbers (i.e. momentum + spin), but instead a centre of mass momentum together with an infinity of Fourier coefficients to completely describe a general excitation of e.g. a closed string. Much more data is needed to create a one-string state from the vacuum in string field theory, than to create a basic point-state or one-particle momentum eigenstate from the vacuum in ordinary QFT.

Ref:
http://en.wikipedia.org/wiki/String_field_theory

There is no position eigenstate basis that will span the Fock space in the string field theory. This is evident, since this is a quantum theory of closed curves. It is evident from looking at the path-integral formulation, where initial and final states of a quantum amplitude must be chosen as closed curves.

Why do you say "one-particle point states (corresponding to Dirac delta distributions).", why not simply "one-particle states"?

It was a mistake on my part. The state I spoke of is localized to a point, but doesn't have a definite particle number. Products of such states can span the Fock space of ordinary QFT, but not in string field theory.

At least that was my understanding of all this.

 

[tom.stoer]

I agree that there are certain pictures where "zero-dim. particles" vs. "one-dim strings" makes sense, but I think one should not overrate this. I agree that string field theory is looking totally different. I agree that in perturbation theory Feynman diagrams look different and of course position space (wave functionals) look different, too.

All I wanted to say is that the Fock space picture is (on an algebraic level) more or less identical; the differences are due to dynamical symmetries.

Of course the starting points of QFT and string theory "zero-dim. particles" and "one-dim strings", respectively, but in both cases these starting points become almost irrelevant when looking at the actual formulation of the theories.

 

[A. Neumaier]

Is there any experimental verification for the fact that elementary particles are point like and have no extension in space or its just an assumption?
thanks

''pointlike'' just means described by a local relativistic field. It is an assumption that matches experiment remarkably well. It does not mean that elementary particles are not extended - they are, slightly but predicted by the renormalization process of quantum field theory.

 

[tom.stoer]

I think one should list some possible "definitons" of "point-like" and "size" of particles in QFTs
- delta-distribution charge, e.g. "visible" in the Coulomb-term in QED in Coulomb gauge
- 0-dim. = point-like vertices in Feynman diagrams
- electric, magnetic, ... form factors
- scattering cross sections, scattering length, ... (*)
In scattering experiments the "visible size" of a particle is never zero - except when it is sterile i.e. doesn't scatter at all.

 

[A. Neumaier]

I think one should list some possible "definitons" of "point-like" and "size" of particles in QFTs
- delta-distribution charge, e.g. "visible" in the Coulomb-term in QED in Coulomb gauge
- 0-dim. = point-like vertices in Feynman diagrams
- electric, magnetic, ... form factors
- scattering cross sections, scattering length, ... (*)
In scattering experiments the "visible size" of a particle is never zero - except when it is sterile i.e. doesn't scatter at all.

There is nowhere a clear definition matching the usage. I deduced the meaning of pointlike from its actual usage. There it means ''derived from a local relativistic field''. For a full discussion, see the Section ''Are electrons pointlike/structureless?'' in Chapter B3 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#pointlike

 

[tom.stoer]

There is nowhere a clear definition matching the usage. I deduced the meaning of pointlike from its actual usage. There it means ''derived from a local relativistic field''.

That's exactly the problem.

Usually people think about pointlike particles as if there were pointlike particles (literally). They think about one-dim. strings as if there were one-dim. strings (literally). But that's not true.

There is no single experiment showing that particles are pointlike. There are just experiments showing that certain particles behave similar to idealized mathematical concepts described by delta-functions - but even these idealized particles do not "look" pointlike. They have (e.g.) a non-zero cross section which is an area - indicating that their "radius" as seen by a second particle is not zero.

Therefore the term pointlike is misleading, or even closed to nonsense. Your interpretation "derived from a local relativistic field'' is certainly correct, but a rookie will not be able to understand what you are talking about. If the answer is "yes, there are pointlike particles", then one could imagine that there are pintlike paricles (literally) - which is wrong. If the answer is "no, there are no pointlike particles", then one could conclude that there is a substructure (which is not the case), that there are strings (which we do not know). So the answer to this question is ambiguous which indicates that there's already something wrong with the question.

My idea is always the same (regarding virtual particles, pointlike particles, ...); one should explain that there are some idealized mathematical concepts which could be interpreted as something like an "xyz-structure", but these structures do not EXIST, they are not REAL, one must be careful not to take them literally. I Hopethat this becomes clear when looking at an electron:
- with delta-function-like charge density (pointlike)
- with divergent total scattering cross section (infinite)
- with Fock-space description (no "size" at all)
- perhaps with a stringy description (string, ...)

 

[A. Neumaier]

That's exactly the problem.

Usually people think about pointlike particles as if there were pointlike particles (literally).

Yes, but we cannot change widespread usage.

Thus the only way to change this is to teach people that some words have a technical meaning different from what was historically associated with the literal meaning of the word.

 

[ShayanJ]

So you guys want to tell that an e.g. electron has an area but that area is somehow nothing because it should be fundamental.Well I think till now I got used to hear things such strange about quantum world.
I can accept it but can't understand it.The same case about pros too(I think).
thanks