Editing Fermi gas (section)

==Extensions to the model==

===Relativistic Fermi gas===
[[File:ChandrasekharLimitGraph.svg|right|thumb|upright=1.5|Radius–mass relations for a model white dwarf, relativistic relation vs non-relativistic. The [[Chandrasekhar limit]] is indicated as ''M''<sub>Ch</sub>.]]
The article has only treated the case in which particles have a parabolic relation between energy and momentum, as is the case in non-relativistic mechanics. For particles with energies close to their respective [[rest mass]], the equations of [[special relativity]] are applicable. Where single-particle energy is given by:
<math display="block">E=\sqrt{(pc)^2 + (mc^2)^2}.</math>

For this system, the Fermi energy is given by:
<math display="block">E_{\mathrm{F}}=\sqrt{(p_{\mathrm{F}}c)^2+(mc^2)^2}-mc^2\approx p_{\mathrm{F}}c,</math>
where the <math>\approx</math> equality is only valid in the [[ultrarelativistic limit]], and<ref>{{cite book|title=Thermodynamics and Statistical Mechanics|last1=Greiner|first1=Walter |last2=Neise |first2=Ludwig |last3=Stöcker|first3=Horst|date=1995|publisher=Springer, New York, NY|isbn=9780387942995|series=Classical Theoretical Physics|pages=[https://archive.org/details/thermodynamicsst0000grei/page/341 341–386] |language=en|doi=10.1007/978-1-4612-0827-3_14|author-link=Walter Greiner|author-link3=Horst Stöcker |url=https://archive.org/details/thermodynamicsst0000grei/page/341}}</ref>
<math display="block">p_{\mathrm{F}} = \hbar\left(\frac{1}{g_s} 6\pi^2 \frac{N}{V}\right)^{1/3}.</math>

The relativistic Fermi gas model is also used for the description of massive white dwarfs which are close to the [[Chandrasekhar limit]]. For the ultrarelativistic case, the degeneracy pressure is proportional to <math>(N/V)^{4/3}</math>.

===Fermi liquid===
In 1956, [[Lev Landau]] developed the [[Fermi liquid theory]], where he treated the case of a Fermi liquid, i.e., a system with repulsive, not necessarily small, interactions between fermions. The theory shows that the thermodynamic properties of an ideal Fermi gas and a Fermi liquid do not differ that much. It can be shown that the Fermi liquid is equivalent to a Fermi gas composed of collective excitations or [[quasiparticle]]s, each with a different [[effective mass (solid-state physics)|effective mass]] and [[magnetic moment]].