Generalized and Modified Coherent States  

In General > s.a. Squeezed States.
* Idea: Several have been proposed, for systems other than the harmonic oscillator, and they differ considerably.
* Generalized: (Perelomov) A state of the form |g = T(g) |0, where T(g) is a representation of g G.
* Weak: They do not admit a resolution of unity expressed in terms of a local integral; They arise, e.g., in the case that a group acts on an inadmissible fiducial vector.

And Group Theory > s.a. types of coherent states.
@ And group representations: Perelomov CMP(72)mp/02, 86.
@ SU groups: Luo JMP(97), Basu PRS(99) [SU(1,1)]; Mathur & Sen JMP(01)qp/00 [SU(3)]; Barros e Sá JPA(01)qp/00 [SU(2)], Lachièze-Rey et al IJTP(03)mp; de Guise & Bertola JMP(02) [SU(n+1) on Tn]; Nemoto JPA(00)qp, Mathur & Mani JMP(02)qp [SU(n)]; Mathur & Paul JPA(05)qp [with SU(2) and SU(3) charges]; Sadiq & Inomata JPA(07) [polynomial su(2) algebra]; > s.a. quantum theory in phase space [qubits].
@ SO groups: Lindner et al PRA(03)qp [SO(4) states as direction indicators]; Xu & Ye IJMPA(04) [SO(2,1), for Coulomb problem].
@ Euclidean groups: Isham & Klauder JMP(91).
@ On Lie algebras: Antonsen IJTP(99)phy/97; Fujii hp/01, ht/01, qp/01, YMJ(02)qp [on su(2) and su(1,1)].
@ For deformed algebras: Sunilkumar et al qp/99; El Baz et al mp/02; Roknizadeh & Tavassoly JPA(04)mp [f-deformed Fock space]; Kowalski & Rembielinski JPA(04)qp [q-deformed on a circle]; Alvarez-Moraga JPA(05)mp [coherent and squeezed]; Yin & Zhang PLB(05) [in non-commutative space]; Skoda LMP(07) [Hopf algebras].
@ Non-commutative quantum mechanics: Lubo JHEP(04)ht/03; Ben Geloun & Scholtz a0901 [Gazeau-Klauder coherent states].
@ Deformed oscillators: Chung IJTP(01); Nozari & Azizi IJQI(05)gq [harmonic oscillator with generalized uncertainty principle]; El Baz mp/05 [k-deformed fermionic-Grassmann]; Eremin & Meldianov TMP(06), a0810 [and uncertainties].
@ Related topics: Coftas & Gazeau a0803 [finite groups, and crystal structure].

Other Modified Coherent States > s.a. Ladder Operators [systems with continuous spectra].
* Non-linear: Right-hand eigenstates of the product of the boson â operator and a non-linear function of the N operator.
* Thermal: They provide a framework for generalizing the uncertainty relation to take into account both thermal and quantum fluctuations.
@ Non-linear, even/odd: de Matos & Vogel PRA(96) [non-linear]; Man'ko et al PS(97); Mancini PLA(97); Sivakumar PLA(98), JPA(00); Roy & Roy JPA(98), PLA(99), PLA(99), JPB(00), JPB(00); Wang et al IJTP(03), IJTP(03), IJTP(04); Guo et al IJTP(07).
@ Proposals: Mann et al JMP(89) [thermal coherent states]; Klauder AP(95); Brif et al qp/98-in [group theoretic]; Gazeau & Klauder JPA(99); Penson & Solomon JMP(99); Martin Nieto & Truax OC(00)qp/99 [eigenstates of a j]; Trifonov JOSA(00)qp; Watson & Klauder JMP(00)qp [affine]; Fujii ht/01; Avron et al JMP(02)mp [in time-energy plane]; Solovej & Spitzer mp/02, mp/02-in [and Scott's correction]; Thirulogasanthar & Honnouvo IJTP(04)mp/03 [z → f(z)]; Appl & Schiller qp/03 [hypergeometric]; Hartmann ht/03, Hartmann & Klauder JMP(04)ht/03 [weak]; Roknizadeh & Tavassoly JPA(04)qp, JMP(05)qp/04 [generalized from non-linear]; Hassouni et al PRA(05) [algebraic systems]; Tavassoly qp/05 [tutorial]; Bagarello JPA(09)-a0904 [Gazeau-Klauder-type vector coherent states]; Naderi et al IJMPA(09) [and non-commutative geometry].
@ Semi-coherent: & Mathews & Eswaran (73); Dodonov & Renó JPA(06) [properties].
@ Photon added: Quesne PLA(01)qp [on the circle]; > s.a. types of coherent states.
@ Supercoherent states, supersymmetric quantum mechanics: Kochetov PLA(96) [path integral]; Samsonov JMP(97); Akhtarshenas IJTP(96) [parasupersymmetric coherent states]; Fernández et al JPA(07); > s.a. modified quantum mechanics.
@ Evolution: Kovner & Rosenstein PRD(85); Nikolov & Trifonov qp/04.
@ Manifold of (generalized) coherent states: Fujiwara & Nagaoka JMP(99); Fivel qp/02.
@ Comparisons: Crawford JPA(99); Fox & Choi PRA(00) [regular vs Gaussian Klauder].
@ Related topics: Nesterov & Sabinin IJTP(97)ht/00 [loops and geometric phases]; Ali et al qp/03 [dualities and relationships]; Boixo et al EPL(07)qp/06 [for open quantum systems, and noiseless subspaces]; Bang & Berger a0811 [discrete phase space].

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