Editing Fermi liquid theory (section)

===Energy===
The [[energy]] of a many-particle state is not simply a sum of the single-particle energies of all occupied states. Instead, the change in energy for a given change <math>\delta n_k</math> in occupation of states <math>k</math> contains terms both linear and quadratic in <math>\delta n_k</math> (for the Fermi gas, it would only be linear, <math>\delta n_k \varepsilon_k</math>, where <math>\varepsilon_k</math> denotes the single-particle energies). The linear contribution corresponds to renormalized single-particle energies, which involve, e.g., a change in the effective mass of particles. The quadratic terms correspond to a sort of "mean-field" interaction between quasiparticles, which is parametrized by so-called Landau Fermi liquid parameters and determines the behaviour of density oscillations (and spin-density oscillations) in the Fermi liquid. Still, these mean-field interactions do not lead to a scattering of quasi-particles with a transfer of particles between different momentum states.

The renormalization of the mass of a fluid of interacting fermions can be calculated from first principles using many-body computational techniques. For the two-dimensional [[homogeneous electron gas]], [[GW approximation|GW calculations]]<ref>{{cite journal|author1=R. Asgari |author2=B. Tanatar |title= Many-body effective mass and spin susceptibility in a quasi-two-dimensional electron liquid|journal= Physical Review B|volume=74|issue=7 |pages=075301|year=2006|doi= 10.1103/PhysRevB.74.075301|bibcode = 2006PhRvB..74g5301A |url=http://repository.bilkent.edu.tr/bitstream/11693/23741/1/bilkent-research-paper.pdf|hdl=11693/23741 |hdl-access=free}}</ref> and [[quantum Monte Carlo]] methods<ref>{{cite journal|author1=Y. Kwon |author2=D. M. Ceperley |author3=R. M. Martin |title= Quantum Monte Carlo calculation of the Fermi-liquid parameters in the two-dimensional electron gas|journal= Physical Review B|volume= 50
|issue=3 |pages=1684–1694|year=2013|doi= 10.1103/PhysRevB.50.1684|pmid=9976356 |bibcode = 1994PhRvB..50.1684K |arxiv=1307.4009}}</ref><ref>{{cite journal|author1=M. Holzmann |author2=B. Bernu |author3=V. Olevano |author4=R. M. Martin |author5=D. M. Ceperley |title= Renormalization factor and effective mass of the two-dimensional electron gas|journal= Physical Review B|volume= 79 |issue=4 |pages= 041308(R)|year=2009|doi= 10.1103/PhysRevB.79.041308|arxiv = 0810.2450 |bibcode = 2009PhRvB..79d1308H |s2cid=12279058 }}</ref><ref>{{cite journal|author1=N. D. Drummond |author2=R. J. Needs |title= Diffusion quantum Monte Carlo calculation of the quasiparticle effective mass of the two-dimensional homogeneous electron gas|journal= Physical Review B|volume=87 |issue=4 |pages=045131|year=2013|doi= 10.1103/PhysRevB.87.045131|arxiv = 1208.6317 |bibcode = 2013PhRvB..87d5131D |s2cid=53548304 }}</ref> have been used to calculate renormalized quasiparticle effective masses.