In a field theory approach to multi-particle systems, the fermion density is controlled by the value of the fermion chemical potential μ {\displaystyle \mu } . One evaluates the partition function Z {\displaystyle Z} by summing over all classical field configurations, weighted by exp ⁡ ( − S ) {\displaystyle \exp(-S)} where S {\displaystyle S} is the action of the configuration. The sum over fermion fields can be performed analytically, and one is left with a sum over the bosonic fields σ {\displaystyle \sigma } (which may have been originally part of the theory, or have been produced by a Hubbard–Stratonovich transformation to make the fermion action quadratic)