Auxiliary field
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In physics, and especially quantum field theory, an auxiliary field is one whose equations of motion admit a single solution. Therefore, the Lagrangian describing such a field A 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 A is: 
and the Lagrangian becomes: 
. Auxiliary fields do not propagate and hence the content of any theory remains unchanged by adding such fields by hand. If we have an initial Lagrangian 
describing a field 
then the Lagrangian describing both fields is:
.
Therefore, auxiliary fields can be employed to cancel quadratic terms in in and linearize the action 
Examples of auxiliary fields are the complex scalar field F in a chiral superfield, the real scalar field D in a vector superfield, the scalar field B in BRST and the field in the Hubbard-Stratonovich transformation.
[edit] References
- Superspace, or One thousand and one lessons in supersymmetry arXiv:hep-th/0108200
