In quantum field theory, particles are typically treated as excitations of their respective fields. Bosons are particles that have integer spins (0, 1, 2, etc.), while fermions have half-integer spins (1/2, 3/2, etc.). The interactions and excitations of these fields are described by the rules and principles of quantum field theory.
The excitations of boson fields, such as the electromagnetic field (photons), the Higgs field (Higgs boson), or the gluon field (gluons), can occur in the absence of fermions. For example, photons can be generated in processes involving only bosons, such as the decay of a Higgs boson into two photons.
However, it's important to note that certain interactions involving fermions can lead to the creation or annihilation of particles through the exchange of bosons. For instance, in the electroweak interaction, fermions (e.g., electrons) can interact via the exchange of W and Z bosons.
Additionally, in certain cases, the presence of fermions can affect the properties and behavior of boson fields. For example, the Higgs boson interacts with fermions to give them mass through the Higgs mechanism.
In quantum field theory, particles and their interactions are described probabilistically through scattering amplitudes and Feynman diagrams. These calculations involve summing over all possible ways particles can interact and exchange bosons.
Regarding your mention of "random short-lived excitations," it's important to clarify that quantum field theory describes the probabilistic behavior of particles and their interactions. Excitations and interactions occur according to the rules and probabilities prescribed by quantum field theory, rather than being truly random or short-lived. The theory provides a systematic framework for calculating and predicting the probabilities of various particle interactions.
Overall, the excitations of boson fields and their interactions can occur both in the presence or absence of fermions, and they follow the principles and rules of quantum field theory.