In the context of quantum field theory, the term "covariant quantum fields" refers to fields that transform covariantly under certain symmetry transformations. Let's break down the meaning of each term:
Quantum fields: In quantum field theory, physical entities such as particles and forces are described in terms of fields. These fields are mathematical objects that exist throughout spacetime and can be thought of as a set of values assigned to each point in spacetime. Quantum fields are operators that create and annihilate particles and obey specific mathematical rules dictated by the principles of quantum mechanics.
Covariant: In physics, the term "covariant" means that an object transforms in a particular way under a given symmetry transformation. In the context of quantum field theory, it usually refers to transformations under the Lorentz group, which is the group of transformations that preserves the spacetime interval in special relativity. Lorentz transformations include rotations and boosts, which change the coordinates and velocities of objects.
In quantum field theory, the equations governing the behavior of fields, such as the Klein-Gordon equation or the Dirac equation, are formulated in a way that ensures the fields transform covariantly under Lorentz transformations. This is important because it allows the theory to maintain its consistency and preserve important symmetries, such as Lorentz invariance.
In summary, "covariant quantum fields" are fields in quantum field theory that transform in a specific way under Lorentz transformations, preserving the symmetry and consistency of the theory with respect to the principles of special relativity.