An auxiliary field has no kinetic term and can be eliminated algebraically. The complex field in a chiral superfield balances bosonic and fermionic degrees of freedom off shell.
For a real auxiliary field with quadratic Lagrangian density , , the Feynman propagator is the inverse quadratic kernel multiplied by : . It is independent of momentum; in position space it is the contact distribution . Two interaction vertices joined by this auxiliary-field propagator give . Completing the square in produces , proving the equivalence to a local interaction by a Gaussian integral.
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An auxiliary field can refer to a couple of concepts depending on the context in which it is being used. Below are a few interpretations based on different domains: 1. **Mathematics/Physics**: In theoretical physics, particularly in the context of field theories, auxiliary fields are additional fields introduced to simplify calculations or formulate certain theories. For example, in supersymmetry, auxiliary fields can be added to superspace to ensure that certain properties (like invariance) hold true.