相关论文: Coherent States of $SU(l,1)$ groups

In this survey, various generalisations of Glauber-Sudarshan coherent states are described in a unified way, with their statistical properties and their possible role in non-standard quantisations of the classical electromagnetic field.…

It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon states. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed…

We build coherent states (CS) for unbounded motions along two different procedures. In the first one we adapt the Malkin-Manko construction for quadratic Hamiltonians to the motion of a particle in a linear potential. A generalization to…

While dealing with a class of generalized Bergman spaces on the unit ball, we construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the…

We provide a group theory approach to coherent states describing quantum space-time and its properties. This provides a relativistic framework for the metric of a Riemmanian space with bosonic and fermionic coordinates, its continuum and…

The Barut-Girardello coherent states (BG CS) representation is extended to the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson realizations. The sp(N,R) BG CS take the form of multimode ordinary Schr\"odinger cat…

The ladder operator formalism of a general quantum state for su(1,1) Lie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Perelomov's coherent state is a su(1,1) nonlinear…

A new proof for the completeness of the coherent states $D(\alpha )\mid f>$ for the Heisenberg Weyl group and the groups $SU(2)$ and $SU(1,1)$ is presented. Generalizations of these results and their consequences are disussed.

In this paper we present a harmonic oscillator realization of the most degenerate discrete series representations of the SU(2,1) group and the deformation quantization of the coset space $D=SU(2,1)/U(2)$ with the method of coherent state…

We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…

In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow z_D \in…

Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present…

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated…

We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the…

We present a possible construction of coherent states on the unit circle as configuration space. Our approach is based on Borel quantizations on S^1 including the Aharonov-Bohm type quantum description. The coherent states are constructed…

Coherent states for general systems with discrete spectrum, such as the bound states of the hydrogen atom, are discussed. The states in question satisfy: (1) continuity of labeling, (2) resolution of unity, (3) temporal stability, and (4)…

A sufficient condition for a state |\psi> to minimize the Robertson-Schr\"{o}dinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized…

We present a coherent state quantization of the dynamics of a relativistic test particle on a one-sheet hyperboloid embedded in a three-dimensional Minkowski space. The group SO_0(1,2) is considered to be the symmetry group of the system.…

The canonical coherent states are expressed as infinite series in powers of a complex number $z$ in their infinite series version. In this article we present classes of coherent states by replacing this complex number $z$ by other choices,…

We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Catalan numbers. We show that these states satisfy the condition of the resolution of unity in a natural way.…