Editing Coherent state (section)

== Generalizations ==
* According to Gilmore and Perelomov, who showed it independently, the construction of coherent states may be seen as a problem in [[group theory]], and thus coherent states may be associated to groups different from the [[Heisenberg group]], which leads to the canonical coherent states discussed above.<ref>A. M. Perelomov, Coherent states for arbitrary Lie groups, ''Commun. Math. Phys.''  '''26''' (1972) 222-236;
 [https://arxiv.org/abs/math-ph/0203002 arXiv: math-ph/0203002].</ref><ref>A. Perelomov, ''Generalized coherent states and their applications'', Springer, Berlin 1986.</ref><ref>{{cite journal | last=Gilmore | first=Robert | title=Geometry of symmetrized states | journal=Annals of Physics | publisher=Elsevier BV | volume=74 | issue=2 | year=1972 | issn=0003-4916 | doi=10.1016/0003-4916(72)90147-9 | pages=391–463| bibcode=1972AnPhy..74..391G }}</ref><ref>{{cite journal|first=R. |last=Gilmore |title=On properties of coherent states|journal=Revista Mexicana de Física|volume=23|issue=1–2|year=1974|pages=143–187|url=https://rmf.smf.mx/pdf/rmf/23/1y2/23_1y2_143.pdf}}</ref> Moreover, these coherent states may be generalized to [[quantum group]]s. These topics, with references to original work, are discussed in detail in [[Coherent states in mathematical physics]].

* In [[quantum field theory]] and [[string theory]], a generalization of coherent states to the case where infinitely many [[degrees of freedom (physics and chemistry)|degrees of freedom]] are used to define a [[vacuum state]] with a different [[vacuum expectation value]] from the original vacuum.
* In one-dimensional many-body quantum systems with fermionic degrees of freedom, low energy excited states can be approximated as coherent states of a bosonic field operator that creates particle-hole excitations. This approach is called [[bosonization]].
* The Gaussian coherent states of nonrelativistic quantum mechanics can be generalized to ''relativistic coherent states'' of Klein-Gordon and Dirac particles.<ref>G. Kaiser,  ''Quantum Physics, Relativity, and Complex Spacetime: Towards a New Synthesis'', North-Holland, Amsterdam, 1990.</ref><ref>S.T. Ali, J-P. Antoine, and J-P. Gazeau,  ''Coherent States, Wavelets and Their Generalizations'',  Springer-Verlag, New York, Berlin, Heidelberg, 2000.</ref><ref>{{cite journal | last=Anastopoulos | first=Charis | title=Generalized coherent states for spinning relativistic particles | journal=Journal of Physics A: Mathematical and General | volume=37 | issue=36 | date=2004-08-25 | issn=0305-4470 | doi=10.1088/0305-4470/37/36/004 | pages=8619–8637|arxiv=quant-ph/0312025| bibcode=2004JPhA...37.8619A | s2cid=119064935 }}</ref>
* Coherent states have also appeared in works on [[loop quantum gravity]] or for the construction of (semi)classical canonical quantum general relativity.<ref>{{cite journal | last1=Ashtekar | first1=Abhay | last2=Lewandowski | first2=Jerzy | last3=Marolf | first3=Donald | last4=Mourão | first4=José | last5=Thiemann | first5=Thomas | title=Coherent State Transforms for Spaces of Connections | journal=Journal of Functional Analysis | volume=135 | issue=2 | year=1996 | issn=0022-1236 | doi=10.1006/jfan.1996.0018 | pages=519–551|doi-access=free|arxiv=gr-qc/9412014}}</ref><ref>{{cite journal | last1=Sahlmann | first1=H. | last2=Thiemann | first2=T. | last3=Winkler | first3=O. | title=Coherent states for canonical quantum general relativity and the infinite tensor product extension | journal=Nuclear Physics B | publisher=Elsevier BV | volume=606 | issue=1–2 | year=2001 | issn=0550-3213 | doi=10.1016/s0550-3213(01)00226-7 | pages=401–440|arxiv=gr-qc/0102038| bibcode=2001NuPhB.606..401S | s2cid=17857852 }}</ref>