"Covariant quantum fields" refers to a mathematical framework used in quantum field theory (QFT) to describe the behavior of particles and fields in a way that is consistent with the principles of special relativity. The term "covariant" refers to the transformation properties of the fields under Lorentz transformations, which are the mathematical transformations that preserve the form of the laws of physics in different inertial reference frames.
In QFT, fields are described by mathematical objects known as field operators, which are operators that act on a quantum state and create or annihilate particles. These field operators are assigned to each point in spacetime, forming a field throughout space and time.
The concept of covariance in QFT means that the equations describing the fields and their interactions should have the same form in all inertial reference frames. This is important because special relativity states that the laws of physics should be the same for all observers moving at a constant velocity relative to each other.
To achieve covariance, the equations of QFT are formulated using four-dimensional spacetime, where time is treated on an equal footing with the three spatial dimensions. The mathematical framework used to describe these fields is based on the principles of quantum mechanics and special relativity, resulting in a covariant formulation.
By incorporating the principles of special relativity into the framework of quantum field theory, covariant quantum fields provide a consistent description of particle interactions that is compatible with our modern understanding of spacetime and relativistic effects. This allows for the formulation of quantum field theories, such as the standard model of particle physics, that can accurately describe the behavior of particles and fields at high energies and in relativistic regimes.