Luttinger's theorem
![Luttinger's theorem relates a Fermi liquid's particle density to the volume of its Fermi surface.](/Images/godic/202501/25/Fermi_Surface.svg1040.png")
In condensed matter physics, Luttinger's theorem is a result derived by J. M. Luttinger and J. C. Ward in 1960 that has broad implications in the field of electron transport. It arises frequently in theoretical models of correlated electrons, such as the high-temperature superconductors, and in photoemission, where a metal's Fermi surface can be directly observed.