In the Standard Model of particle physics, particles are indeed described as excitations of their corresponding quantum fields. Each elementary particle, such as electrons, quarks, or neutrinos, is associated with its own quantum field.
In the case of the electron, it is associated with the electron field. Excitations of this field correspond to the presence of electrons in different energy states. These energy states are quantized, meaning they can only have specific values. The different energy states of the electron field are often referred to as electron energy levels or electron states.
When an electron transitions between different energy levels within the electron field, it can emit or absorb photons, which are quanta of the electromagnetic field. The energy of the emitted or absorbed photon corresponds to the energy difference between the initial and final states of the electron.
So, just like photons can have different energy levels, electrons can also exist in different energy levels within their associated quantum field. The specific energy levels available to electrons depend on the specific system or environment in which they are located, such as an atom or a solid material with its energy band structure.
It's worth noting that the behavior of electrons and their energy levels can be described using quantum mechanics and quantum field theory. The mathematics of these theories allows us to calculate and predict the possible energy levels and transitions of electrons within their quantum fields, providing a powerful framework for understanding the behavior of subatomic particles.