what are point particles? are they three dimensional spheres?

Answer 1

The concept of a "point particle" is a purely theoretical construct for *effective* theories of matter, such as the standard model of particle physics. It simply means that internal structure, if any, is not taken into account in the theory, but there is no presumption of ultimate truth associated with that assertion. Therefore, no, there is no implication that they are three dimensional spheres or any other shape; that would be an assumption related to internal structure which, as stated, is neglected. If string theory (an attempt at a more fundamental theory) has anything to it, there are no *actual* point particles, only 11 dimensional strings.

Answer 2

In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle.

The field’s action on the particle is difficult to calculate because of its singular nature: The field diverges at the position of the particle. But it is possible to isolate the field’s singular part and show that it exerts no force on the particle - its only effect is to contribute to the particle’s inertia. What remains after subtraction is a smooth field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free (radiative) field that interacts with the particle; it is this interaction that gives rise to the self-force.

Answer 3

A point particle is just that - a particle with no extent at all in x, y or z. In other words, they have no 3D extent. The standard model of quantum mechanics assumes all fundamental particles (quarks and leptons) are point particles.

Answer 4

Quarks, presumed to have no dimensions at all, just a point in space.