Numerical sign problem: Difference between revisions

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Revision as of 08:38, 8 February 2011

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(References for this section: <ref name='Wiese-cluster'/>,<ref name='Kieu'/>).

In a field theory approach to multi-particle systems, the fermion density is controlled by the value of the fermion [[chemical potential]] <math>\mu</math>. One evaluates the [[Partition_function_(quantum_field_theory)|partition function]] <math>Z</math> by summing over all classical field configurations, weighted by <math>\exp(-S)</math> where <math>S</math> is the [[action]] of the configuration. The sum over fermion fields can be performed analytically, and one is left with a sum over the [[Boson|bosonic]] fields <math>\sigma</math> (which may have been originally part of the theory, or have been produced by a [[Hubbard-Stratonovich transformation]] to make the fermion action quadratic)

:<math>Z = \int D \sigma \; \rho[\sigma]</math>