Quantum fields are indeed considered to be physical entities in modern physics. They are fundamental concepts in quantum field theory, which is a theoretical framework that combines quantum mechanics and special relativity to describe the behavior of elementary particles and their interactions.
In the framework of quantum field theory, fields are not considered to be made of anything more fundamental. They are treated as fundamental entities themselves. According to our current understanding, quantum fields are not composed of smaller constituents or building blocks. They are fundamental properties of space and are pervasive throughout the universe.
Regarding the notion of quantum fields being made of energy, it's important to clarify the distinction between fields and their associated energy. Quantum fields can carry energy, but they are not solely composed of energy. Energy is a property that can be associated with the excitations or fluctuations of a quantum field. These excitations, often referred to as particles, correspond to quantized energy states of the field.
Our best theories, such as the Standard Model of particle physics, describe the nature of quantum fields and their interactions. According to these theories, quantum fields permeate all of spacetime and interact with particles, giving rise to various fundamental forces and particles we observe in the universe. These fields are described mathematically using specific equations, such as the Dirac equation for fermionic fields or the Klein-Gordon equation for scalar fields.
Quantum field theory treats fields as dynamic entities, subject to quantum fluctuations and interactions. The theory allows for the creation and annihilation of particles, as well as the exchange of virtual particles between interacting particles. This framework has been extremely successful in describing the behavior of elementary particles and has been extensively tested through experiments.
However, it's worth noting that our understanding of quantum fields and their fundamental nature is based on theoretical models and empirical observations. The ultimate nature of quantum fields and their relationship to other fundamental aspects of the universe, such as spacetime or the nature of reality itself, is still an active area of research and subject to ongoing scientific investigation.