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Partition function (quantum field theory)
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<p>In <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, partition functions are <a href="/facts/Generating_function/K7UVjnjL">generating functionals</a> for <a href="/facts/Correlation_function_(quantum_field_theory)/zH7RInAw">correlation functions</a>, making them key objects of study in the <a href="/facts/Path_integral_formulation/6lt2MHkW">path integral formalism</a>. They are the <a href="/facts/Imaginary_time/UTTYSUw7">imaginary time</a> versions of <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a> <a href="/facts/Partition_function_(statistical_mechanics)/q65sJrrn">partition functions</a>, giving rise to a close connection between these two areas of physics. Partition functions can rarely be solved for exactly, although <a href="/facts/Free_field/gQCzm5KU">free theories</a> do admit such solutions. Instead, a <a href="/facts/Perturbation_theory_(quantum_mechanics)/lYGgk9Ph">perturbative</a> approach is usually implemented, this being equivalent to summing over <a href="/facts/Feynman_diagram/BRFNvDdr">Feynman diagrams</a>. </p>