The electron is indicated as Fermion and as such an elementary particle in The Standard Model.
The electron and the subsequent generations muon and tau are studied and described in detail in the scientific literature. We use as starting position the first assessment as in Wikipedia as reference:
The electron is a subatomic particle, symbol e− or β−, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton.] Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. As it is a fermion, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.
This introduction has many references with links to specific descriptions of notions. The information in Wikipedia regarding the electron refers to 181 sources.
Quantum Physics challenges the assumption of an electron as a point particle in so far that a non zero volume for point particles in general, is questioned.
The electron shows a specific behavior called spinor. That spinor is rather complex in its driving forces and “mechanism.” There are only some complex models available for clarification of this functionality.
The Wikipedia description of the spinor is:
In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation When a sequence of such small rotations is composed (integrated) to form an overall final rotation, however, the resulting spinor transformation depends on which sequence of small rotations was used: unlike vectors and tensors, a spinor transforms to its negative when the space is rotated through a complete turn from 0° to 360° (see picture). This property characterizes spinors. It is also possible to associate a substantially similar notion of spinor to Minkowski space in which case the Lorentz transformations of special relativity play the role of rotations. Spinors were introduced in geometry by Élie Cartan in 1913. In the 1920s physicists discovered that spinors are essential to describe the intrinsic angular momentum, or “spin”, of the electron and other subatomic particles.
There are models available like:
As per Richard Feynman
Alternatively, more elaborated
A mathematical description is in Clifford Algebra. The description of the spinor is sufficient for technical applications.
We can conclude: the electron itself has very complex spatial manifestations, and not all are well understood and/or modeled yet.
With all these complex manifestations, we need to question: for what reasons is an electron identified as a fundamental point particle?
The next chapter will handle this question.