Point particle
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A point particle is an idealized object heavily used in physics. Its defining feature is that it lacks spatial extension: being zero dimensional, it does not take up space. A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. In Newtonian gravitation and classical electromagnetism, for example, the respective fields outside of a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere.
In general relativity a point particle with mass only "exists" in the sense of "test particle", inasmuch as its influence on the curvature of spacetime must be ignored. (Otherwise it would be a black hole instead.)
In particle physics, whose theoretical framework is relativistic quantum mechanics (a.k.a. quantum field theory), "point particle" is synonymous with "elementary particle", which is defined as a particle without structure or, equivalently, as a particle lacking component parts. According to the Standard Model (of fundamental particles and forces), quarks, electrons and other leptons are point particles in this sense.
The question of whether an elementary particle actually has the form of a geometrical point, or is instead a formless object, is of purely metaphysical character, inasmuch as (i) nothing in the theoretical framework of particle physics literally refers to the shape of an elementary particle, whereas (ii) experiments may or may not furnish evidence of a particle's structure but cannot furnish evidence of the absence of structure. In other words, neither theory nor experiment can distinguish between a particle with a pointlike shape and a particle that lacks a shape.