In a field-theory approach to multi-particle systems, the fermion density is controlled by the value of the fermion chemical potential μ μ . One evaluates the partition function Z by summing over all classical field configurations, weighted by exp ⁡ ⁡ ( − − S ) , where 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 σ (which may have been originally part of the theory, or have been produced by a Hubbard–Stratonovich transformation to make the fermion action quadratic)