# Coherent states for arbitrary Lie group

@article{Perelomov1972CoherentSF, title={Coherent states for arbitrary Lie group}, author={Askold M. Perelomov}, journal={Communications in Mathematical Physics}, year={1972}, volume={26}, pages={222-236} }

The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.

#### 1,014 Citations

A note on coherent state representations of Lie groups

- Mathematics
- 1975

The analyticity properties of coherent states for a semisimple Lie group are discussed. It is shown that they lead naturally to a classical ’’phase space realization’’ of the group.

Coherent state representations of nilpotent Lie groups

- Mathematics
- 1977

The coherent state representations of a connected and simply connected nilpotent Lie group are characterized in terms of the Kirillov correspondence, as being those irreducible unitary… Expand

Generalized definition of coherent states and dynamical groups

- Mathematics
- 1975

It is shown that coherent states may be defined for an arbitrary dynamical (Hamiltonian) quantum system and the definition is consistent with the requirement that the Hamiltonian commutes with a Lie… Expand

Coherent states and symmetric spaces

- Mathematics
- 1975

Properties of system of the coherent states related to representations of the class I of principal series of the motion groups of symmetric spaces of rank 1 have been studied. It has been proved that… Expand

Realization of coherent state Lie algebras by differential operators

- Mathematics, Physics
- 2005

A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on K\"ahler coherent state orbits is presented. Explicit formulas involving… Expand

Coherent states and the classical limit on irreducible representations

- Mathematics
- 1998

We give an explicit construction of the coherent states for an arbitrary irreducible representation. We also construct the symplectic structure on the manifold of coherent states, find canonical… Expand

Symplectic orbits in quantum state space

- Physics
- 1990

All symplectic orbits of the action of an arbitrary compact connected Lie group on the space of density operators are found. It is shown that there is only one orbit that is Kahler (orbit of coherent… Expand

Stability of coherent states

- Mathematics
- 1985

The authors give an algebraic characterisation of the dynamical systems which preserve the coherence of a generalised coherent state defined for a Lie group. The breaking of coherence is related to… Expand

New coherent states and inhomogeneous differential realization of Lie superalgebra B(0,1)

- Physics
- 1993

New coherent states for the Lie superalgebra B(0,1) are presented. An inhomogeneous differential realization (IHDR) of the Lie superalgebra is obtained. This IHDR may be useful for the study of… Expand

Coherent states and bounded homogeneous domains

- Mathematics
- 1974

Abstract The system of coherent states for complex bounded homogeneous domains is constructed and the properties of coherent states are investigated. The question of selecting complete subsystems… Expand

#### References

SHOWING 1-10 OF 20 REFERENCES

New “Coherent” States associated with non-compact groups

- Mathematics
- 1971

Generalized “Coherent” States are the eigenstates of the lowering and raising operators of non-compact groups. In particular the discrete series of representations ofSO (2, 1) are studied in detail:… Expand

Special Functions and the Theory of Group Representations

- Physics, Mathematics
- 1968

A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible… Expand

The Quantum Theory of Optical Coherence

- Physics
- 1963

The concept of coherence that was conventionally used in optics is found to be inadequate to the needs of recently opened areas of experiment. To provide a fuller discussion of coherence, a… Expand

Gruppentheorie und Quantenmechanik. Leipzig: S.Hirzel 1928

- 1928

Algebraic groups and discontinuous subgroups, p.361

- Proc. Symp. Pure Math.,
- 1966

Commun. Math. Phys

- Commun. Math. Phys
- 1971

Theoret. Math. Phys

- Theoret. Math. Phys
- 1971