Editing Condensed matter physics (section)

===Symmetry breaking===
{{Main|Symmetry breaking}}

Some states of matter exhibit ''symmetry breaking'', where the relevant laws of physics possess some form of [[Symmetry (physics)|symmetry]] that is broken. A common example is [[crystal|crystalline solid]]s, which break continuous [[translational symmetry]]. Other examples include magnetized [[ferromagnetism|ferromagnets]], which break [[rotational symmetry]], and more exotic states such as the ground state of a [[BCS theory|BCS]] [[superconductor]], that breaks [[U(1)]] phase rotational symmetry.<ref>{{cite web |url = https://www.nobelprize.org/nobel_prizes/physics/laureates/2008/nambu-lecture.html |title= Spontaneous Symmetry Breaking in Particle Physics: a Case of Cross Fertilization |last= Nambu |first= Yoichiro |date= 8 December 2008 |website= Nobelprize.org }}</ref><ref>{{cite journal |last=Greiter |first=Martin |arxiv=cond-mat/0503400 |title=Is electromagnetic gauge invariance spontaneously violated in superconductors? |date=16 March 2005 |doi=10.1016/j.aop.2005.03.008 |volume=319 |issue=2005 |journal=Annals of Physics |pages=217–249 |bibcode=2005AnPhy.319..217G |s2cid=55104377 }}</ref>

[[Goldstone's theorem]] in [[quantum field theory]] states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone [[boson]]s. For example, in crystalline solids, these correspond to [[phonon]]s, which are quantized versions of lattice vibrations.<ref name=goldstone>{{cite journal|last=Leutwyler|first=H.|title=Phonons as Goldstone bosons|journal= Helv. Phys. Acta  |volume=70|issue=1997|year=1997|arxiv=hep-ph/9609466|bibcode= 1996hep.ph....9466L|pages=275–286}}</ref>