In quantum electrodynamics (QED), the theory describing the electromagnetic interaction, an electron emitting photons is described by a process called "electron-photon interaction." However, it's important to note that the language of "emitting photons from nothing" can be misleading.
In QED, interactions between particles are described by Feynman diagrams, which are graphical representations of the various possible processes. In the case of electron-photon interaction, the Feynman diagram involves an electron line interacting with a photon line. The electron emits a photon, and the electron's trajectory is modified due to this interaction.
Quantum field theory describes particles as excitations of underlying fields. In the case of QED, the electron is associated with an electron field, and the photon is associated with an electromagnetic field. Interactions occur through the exchange of virtual particles, in this case, virtual photons.
In the quantum world, particles can temporarily borrow energy from the vacuum and exist as virtual particles for very short periods of time, as allowed by the Heisenberg uncertainty principle. In the context of electron-photon interaction, the electron can emit a virtual photon, creating a disturbance in the electromagnetic field. This disturbance propagates as a virtual particle and may be absorbed by another charged particle, resulting in a real photon.
It's important to note that virtual particles, including virtual photons, are mathematical constructs used to describe interactions in quantum field theory. They do not have all the properties of real particles and are not directly observable. The language of "emitting photons from nothing" is a simplified way to describe these processes, but it should be understood within the context of the mathematical formalism of quantum field theory.