The transformation of auxiliary field is used to simplify the mathematical expressions in certain physical theories, such as supersymmetry and gauge theories.
In supersymmetry, the auxiliary field is transformed into a spinor field, which is a fundamental component of the supersymmetry algebra. This transformation allows for the cancellation of unphysical degrees of freedom in the theory.
In gauge theories, the auxiliary field is transformed into a gauge field, which mediates the interactions between particles. This allows for the theory to be invariant under local gauge transformations.
The transformation of auxiliary field can lead to a simpler and more elegant form of the equations of motion in a theory. It can also help to reveal hidden symmetries and relationships between different physical quantities.
Yes, there are limitations to transforming auxiliary field. It may not be possible in all theories, and even when it is possible, the transformed theory may not always be physically meaningful. It is important to carefully consider the implications and consequences of such transformations in a given theory.