# Generalized Coherent States and Their Applications

@inproceedings{Perelomov1986GeneralizedCS, title={Generalized Coherent States and Their Applications}, author={Askold M. Perelomov}, year={1986} }

I Generalized Coherent States for the Simplest Lie Groups.- 1. Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom.- 1.1 The Heisenberg-Weyl Group and Its Representations.- 1.1.1 The Heisenberg-Weyl Group.- 1.1.2 Representations of the Heisenberg-Weyl Group.- 1.1.3 Concrete Realization of the Representation T?(g).- 1.2 Coherent States.- 1.3 The Fock-Bargmann Representation.- 1.4 Completeness of Coherent-State Subsystems.- 1.5 Coherent States and Theta…

## 3,379 Citations

### SU(1,1) Nonlinear Coherent States

- Mathematics, Physics
- 2012

The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the…

### Generalized Coherent States

- Physics
- 2016

In quantum physics coherent states are quantum states which have properties that closely resemble classical description. This thesis studies the notion of generalized coherent states, also called…

### D ec 2 00 1 Introduction to Coherent States and Quantum Information Theory

- Physics
- 2001

The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to…

### Introduction to Coherent States and Quantum Information Theory

- Physics
- 2001

The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to…

### Generalized coherent states for polynomial Weyl-Heisenberg algebras

- Mathematics
- 2012

It is the aim of this paper to show how to construct a la Perelomov and a la Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This algebra depends on r parameters. For some…

### Coherent states: A general formalism

- Physics
- 1993

We present a general formalism for the construction of coherent states, based on the notion of reproducing triple. It covers the case of continuous frames in Hilbert space, as well as generalized…

### Introduction to Coherent States

- PhysicsTheoretical and Mathematical Physics
- 2021

In this Chapter we study the Weyl–Heisenberg group in the Schrodinger representation in arbitrary dimension n. One shows that it operates in the Hilbert space of quantum states (and on quantum…

### Duality of two types of SU(1, 1) coherent states and an intermediate type

- Physics
- 2003

The two types of SU(1, 1) coherent states of Barut and Girardello and of Perelomov are dual in a sense that the operators in the eigenvalue equation and in the exponentials which create these types…

### Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras

- Physics, Mathematics
- 2017

The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form; and (2) to…