auxiliaryfield
An auxiliary field is a field introduced into a theoretical framework to simplify calculations or to expose collective degrees of freedom, without being a primary physical observable of interest. In quantum many-body and quantum field theories, auxiliary fields are often used to convert interacting problems into more tractable ones by decoupling nonlinear interactions.
A common method is the Hubbard–Stratonovich transformation, which introduces an auxiliary (bosonic) field to replace a
In condensed matter and lattice gauge theories, auxiliary fields underpin various decoupling strategies. For example, in
Dynamic versus static variants exist: auxiliary fields can depend on imaginary time (dynamic) or be time-independent
Overall, auxiliary fields are a versatile mathematical tool that enable tractable formulations and numerical approaches for