Charge is indeed a fundamental property of particles in the standard model of particle physics. It is not a result of interactions with other particles or fields, but rather an intrinsic property of the particles themselves.
In the standard model, particles are classified into two broad categories: fermions and bosons. Fermions are the building blocks of matter, including quarks (which make up protons and neutrons) and leptons (such as electrons and neutrinos). Bosons are particles that mediate the fundamental forces, such as photons for electromagnetism or W and Z bosons for the weak nuclear force.
Charge is associated with a specific type of interaction called electromagnetism. Electromagnetism is described by quantum electrodynamics (QED), a part of the standard model. According to QED, electric charge is a property that determines how a particle interacts with the electromagnetic field.
In QED, particles with electric charge, such as electrons and quarks, interact with the electromagnetic field by exchanging photons. For example, an electron can emit or absorb a photon, which represents the exchange of electromagnetic energy and momentum. These interactions give rise to phenomena such as the repulsion between like charges and the attraction between opposite charges.
The charge of a particle is quantized, meaning it can only take certain discrete values. The electric charge of an electron is -1 elementary charge (e), while the up quark has a charge of +2/3 e and the down quark has a charge of -1/3 e. The conservation of electric charge is a fundamental principle in the standard model, which means the total electric charge of a closed system remains constant in any physical process.
Charge is not something that arises from interactions with other particles or fields. It is considered a fundamental property of particles, similar to their mass or spin. It is an intrinsic property that characterizes how particles interact with the electromagnetic field and underlies the fundamental forces and interactions we observe in nature.