In quantum physics, there is no direct concept of "field density" in the same sense as classical physics, where we can talk about the density of a continuous field. Quantum physics describes physical systems in terms of discrete entities, such as particles or quantum fields, and their associated wavefunctions or state vectors.
In quantum field theory (QFT), which combines quantum mechanics with special relativity, fields are described by operators acting on a quantum state. These fields can be associated with particles, and their excitations are quantized as particles with specific properties, such as energy, momentum, and spin. In this framework, we typically talk about particle densities rather than field densities.
For example, in quantum electrodynamics (QED), the quantum field theory describing the electromagnetic force, we can talk about the density of photons, which are the quanta or particles associated with the electromagnetic field. However, even in this case, we describe the density of photons in terms of their number or probability distributions rather than a continuous field density.
It's worth noting that there are quantities related to fields in quantum field theory that have a statistical interpretation, such as the expectation value of a field operator or the vacuum expectation value. However, these quantities are not strictly analogous to a classical field density and have different physical interpretations.
In summary, while quantum field theory deals with fields and their associated particles, the notion of field density in the classical sense does not directly translate to the quantum description, where we typically discuss particle densities or statistical properties of fields.