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?
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.
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.The Fock space is spanned by states created via creation operators.
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"?
''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.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?
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://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html#pointlikeI 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.
That's exactly the problem.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''.
Yes, but we cannot change widespread usage.That's exactly the problem.
Usually people think about pointlike particles as if there were pointlike particles (literally).