In quantum field theory, fundamental particles are indeed considered as excitations of their respective quantum fields. However, it's important to note that the creation and annihilation of particles are processes that occur within the context of interactions described by the theory.
According to quantum field theory, the creation of particles typically involves the interaction of fields. For example, in the context of the electromagnetic interaction, the photon field can give rise to the creation or annihilation of electron-positron pairs through processes such as photon absorption or emission. However, these processes are governed by certain conservation laws, such as conservation of electric charge, energy, and momentum.
In the case you mentioned, one electron field creating two electrons, this process would violate the conservation of electric charge unless there is another particle involved that carries the opposite charge. For example, in the context of the weak nuclear interaction, an electron neutrino field can interact with an electron field to create an electron and an electron antineutrino. This process conserves electric charge, as the total charge before and after the interaction remains the same.
It's important to emphasize that the behavior of quantum fields and the creation and annihilation of particles are described by mathematical equations and governed by the principles of quantum field theory. These principles, including conservation laws, symmetries, and interaction terms, play a crucial role in determining the possibilities and probabilities of particle creation and annihilation processes.