Quantum fields are mathematical constructs used to describe the behavior of particles and their interactions in the framework of quantum field theory. They are fundamental to our current understanding of particle physics. However, whether they should be considered as physical structures or just mathematical concepts is a matter of interpretation and depends on the philosophical perspective one takes.
From a mathematical perspective, quantum fields are mathematical objects that exist within the framework of quantum field theory. They are fields defined at every point in spacetime, and their values represent the quantum properties of particles. These fields satisfy certain mathematical equations, such as the Klein-Gordon equation or the Dirac equation, which govern their behavior.
On the other hand, many physicists interpret quantum fields as representing physical entities that exist in spacetime. According to this view, the fields are not merely abstract mathematical constructs, but rather they correspond to the underlying physical reality of particles and their interactions. In this interpretation, particles are considered excitations or quanta of the quantum fields.
It's worth noting that the precise ontological status of quantum fields is still a topic of debate and active research in physics and philosophy. Different interpretations of quantum mechanics and quantum field theory offer different perspectives on the nature of these fields. Ultimately, the interpretation of quantum fields as physical structures or mathematical concepts depends on one's philosophical stance and the particular interpretation of quantum theory they adhere to.