The charges of elementary particles, such as quarks and electrons, are determined by their interactions with the fundamental forces in nature. In the case of electric charge, it arises from the electromagnetic interaction.
In the Standard Model of particle physics, quarks and electrons are described as having fractional electric charges. Quarks come in different flavors, such as up, down, charm, strange, top, and bottom, each with its respective charge. Up-type quarks (up, charm, top) have a charge of +2/3 e, while down-type quarks (down, strange, bottom) have a charge of -1/3 e. Electrons, along with other charged leptons like muons and taus, have a charge of -e, where e is the elementary charge.
The specific values of these charges are determined by the symmetries and gauge structures of the Standard Model. The Standard Model is based on the principles of local gauge symmetry, which requires that the interactions between particles are invariant under certain symmetry transformations. The electromagnetic force is described by the gauge symmetry of quantum electrodynamics (QED), which is based on the U(1) symmetry.
In QED, the electric charge arises from the coupling of particles to the electromagnetic field mediated by the photon. The fractional charges of quarks and the charge of electrons are consequences of the gauge symmetry and the way these particles interact with the electromagnetic field. The fractional charges of quarks play a crucial role in explaining the behavior of hadrons, composite particles made of quarks.
It's worth noting that the origins of the fundamental charges and the symmetries governing them are still areas of active research in theoretical physics. While the Standard Model successfully describes the behavior of elementary particles and their charges, it is considered an effective theory and is expected to be part of a more comprehensive framework that can explain the origins of these fundamental properties.