Coherent states for SU(3) (original) (raw)

D ec 2 00 0 Coherent States For SU ( 3 )

2004

We define coherent states for SU(3) using six bosonic creation and annihilation operators. These coherent states are explicitly characterized by six complex numbers with constraints. For the completely symmetric representations (n, 0) and (0, m), only three of the bosonic operators are required. For mixed representations (n,m), all six operators are required. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties. We introduce an explicit parameterization of the group SU(3) and the corresponding integration measure. Finally, we discuss the path integral formalism for a problem in which the Hamiltonian is a function of SU(3) operators at each site. PACS: 02.20.-a

Coherent states withSU(2) andSU(3) charges

Journal of Physics A: Mathematical and General, 2005

We define coherent states carrying SU(N) charges by exploiting generalized Schwinger boson representation of SU(N) Lie algebra. These coherent states are defined on 2 (2 N −1 − 1) complex planes. They satisfy continuity property and provide resolution of identity. We also exploit this technique to construct the corresponding non-linear SU(N) coherent states.

Bloch sphere-like construction of SU (3) Hamiltonians using unitary integration

Journal of Physics A: Mathematical and Theoretical, 2009

The Bloch sphere is a familiar and useful geometrical picture of the time evolution of a single spin or a quantal two-level system. The analogous geometrical picture for three-level systems is presented, with several applications. The relevant SU(3) group and su(3) algebra are eight-dimensional objects and are realized in our picture as two four-dimensional manifolds that describe the time evolution operator. The first, called the base manifold, is the counterpart of the S 2 Bloch sphere, whereas the second, called the fiber, generalizes the single U(1) phase of a single spin. Now four-dimensional, it breaks down further into smaller objects depending on alternative representations that we discuss. Geometrical phases are also developed and presented for specific applications. Arbitrary time-dependent couplings between three levels or between two spins (qubits) with SU(3) Hamiltonians can be conveniently handled through these geometrical objects.

SU (3) revisited

Journal of Physics A: Mathematical and General, 1998

The "D" matrices for all states of the two fundamental representations and octet are shown in the generalized Euler angle parameterization. The raising and lowering operators are given in terms of linear combinations of the left invariant vector fields of the group manifold in this parameterization. Using these differential operators the highest weight state of an arbitrary irreducible representation is found and a description of the calculation of Clebsch-Gordon coefficients is given.

Analytic representations based on SU (1 , 1) coherent states and their applications

Journal of Physics A: Mathematical and General, 1996

We consider two analytic representations of the SU (1, 1) Lie group: the representation in the unit disc based on the SU (1, 1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU (1, 1) lowering generator. We show that these representations are related through a Laplace transform. A 'weak' resolution of the identity in terms of the Perelomov SU (1, 1) coherent states is presented which is valid even when the Bargmann index k is smaller than 1 2. Various applications of these results in the context of the two-photon realization of SU (1, 1) in quantum optics are also discussed.

Coherent states in complex variables SU(2S+1)/SU(2S)*U(1)and classical dynamics

arXiv (Cornell University), 2011

Path integral in the representation of coherent states for groups SU(2),SU(3), SU(4) and in general form for SU(n) and its classical consequence are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for transition amplitude which connects a pair of SU(n) coherent states. In the classical limit we arrive at a canonical equation of motion.

Fock–Bargmann space and SU(3) models

Physics of Particles and Nuclei - PHYS PART NUCLEI, 1998

The aim of this review is to present an approach to unitary models that has been developed during the last ten years. The approach uses wave functions and operators defined in Fock-Bargmann space. A solution for the 8U(3) shell model is introduced, as well as some extensions that are related to a classical treatment of 8U (3) theory.

Coherent-state path integrals in the continuum: The SU(2) case

Annals of Physics, 2016

We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.

Quantum Dynamics on the Su (2) Group

2005

In this paper we study the quantum evolution of a wave function defined on the SU(2) group using path integrals. We use an intrinsic approach based on integration over tangent spaces of the group which represents the infinitesimal contribution to the integral. We obtain finally an expression for the Feynman propagator.