Auxiliary field

In physics, and especially quantum field theory, an auxiliary field is one whose equations of motion admit a single solution.

contains an algebraic quadratic term and an arbitrary linear term, while it contains no kinetic terms (derivatives of the field): The equation of motion for

is and the Lagrangian becomes Auxiliary fields generally do not propagate,[1] and hence the content of any theory can remain unchanged in many circumstances by adding such fields by hand.

, then the Lagrangian describing both fields is Therefore, auxiliary fields can be employed to cancel quadratic terms in

The quantum mechanical effect of adding an auxiliary field is the same as the classical, since the path integral over such a field is Gaussian.