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su(1,1)-コヒーレント状態としてのコーシー・ウェーブレット : それに関連した生成消滅関係とInteracting Fock Spaceの関係(第8回「非平衡系の統計物理」シンポジウム,研究会報告)

Fuminori Sakaguchi, Masahito Hayashi

Published Feb 20, 2001• 0 citations
OpenAlex

Abstract

A kind of annihilation/creation relation related to the coherent states associated with the irreducible unitary representation of the affine group is reinterpreted as an annihilation/creation relation associated with the irreducible unitary representation of the algebra su(1,1), by adding another generator to the two generators of the unitary representation of the affine group.

Related papers

su(1,1)-コヒーレント状態としてのコーシー・ウェーブレット : それに関連した生成消滅関係とInteracting Fock Spaceの関係(第8回「非平衡系の統計物理」シンポジウム,研究会報告)

Fuminori Sakaguchi, 正人 林

物性研究•Feb 20, 2001•0 citations

Cauchy wavelets in Terms of su(1,1)-Coherent States(The 8th Symposium on Non-Equilibrium Statisitical Physics)

Fuminori Sakaguchi, Masahito Hayashi

A kind of annihilation/creation relation related to the coherent states associated with the irreducible unitary representation of the affine group is reinterpreted as an annihilation/creation r,elation associated with the irreducible unitary representation of the algebra su(l,l), by adding another generator to the two generators of the unitary representation of the affine group ..

•Feb 20, 2001•0 citations

SU (N) coherent states

Manu Mathur, Hamdi Mani

We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using 2(2N−1−1) bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labeled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.

arXiv:quant-ph/0206005•Journal of Mathematical Physics•Oct 24, 2002•26 citations

Coherent states for the harmonic series irreducible representations of U(p,q). I. Unitary operator coherent states

C. Quesne

Unitary operator coherent states, as defined by Klauder (1963), Perelomov (1972) and Gilmore (1974), are considered for the harmonic series irreducible representations of U(p,q). Various properties of these states are reviewed, including their reproducing kernel and measure explicit forms, as well as the representation they lead to for the U(p,q) generators. Starting from a contraction of the su(p,q) Lie algebra, both Dyson and Holstein-Primakoff boson realisations of u(p,q) are obtained in terms of pq pairs of boson creation, annihilation operators and of the generators of a U(p)*U(q) intrinsic group. Such boson realisations are applied to determine the matrix elements of the U(p,q) generators between discrete bases classified according to the chain U(p,q) contains/implies U(p)*U(q). Finally, the isomorphism between so(4,2) and su(2,2) is employed to derive the corresponding properties of the SO(4,2) unitary operator coherent states for application in atomic physics.

Journal of Physics A Mathematical and General•Mar 11, 1987•2 citations

Cauchy wavelets in Terms of su(1,1)-Coherent States (研究会報告 第8回「非平衡系の統計物理」シンポジウム)

Fuminori Sakaguchi, 正人 林

物性研究•Feb 1, 2001•0 citations

ON A q-FOCK SPACE AND ITS UNITARY DECOMPOSITION

Un-Cig Ji, Young-Yi Kim

A Fock representation of q-commutation relation is studied by constructing a q-Fock space as the space of the representation, the q-creation and q-annihilation operators (-1 < q < 1). In the case of 0 < q < 1, the q-Fock space is interpolated between the Boson Fock space and the full Fock space. Also, a unitary decomposition of the q-Fock space $(q\;{\neq}\;0)$ is studied.

Bulletin of the Korean Mathematical Society•Feb 1, 2006•1 citation
A kind of annihilation/creation relation related to the coherent states associated with the irreducible unitary representation of the affine group is reinterpreted as an annihilation/creation relation associated with the irreducible unitary representation of the algebra su(1,1), by adding another generator to the two generators of the unitary representation of the affine group.
We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using 2(2N−1−1) bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labeled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.
Unitary operator coherent states, as defined by Klauder (1963), Perelomov (1972) and Gilmore (1974), are considered for the harmonic series irreducible representations of U(p,q). Various properties of these states are reviewed, including their reproducing kernel and measure explicit forms, as well as the representation they lead to for the U(p,q) generators. Starting from a contraction of the su(p,q) Lie algebra, both Dyson and Holstein-Primakoff boson realisations of u(p,q) are obtained in terms of pq pairs of boson creation, annihilation operators and of the generators of a U(p)*U(q) intrinsic group. Such boson realisations are applied to determine the matrix elements of the U(p,q) generators between discrete bases classified according to the chain U(p,q) contains/implies U(p)*U(q). Finally, the isomorphism between so(4,2) and su(2,2) is employed to derive the corresponding properties of the SO(4,2) unitary operator coherent states for application in atomic physics.
A Fock representation of q-commutation relation is studied by constructing a q-Fock space as the space of the representation, the q-creation and q-annihilation operators (-1 < q < 1). In the case of 0 < q < 1, the q-Fock space is interpolated between the Boson Fock space and the full Fock space. Also, a unitary decomposition of the q-Fock space (q  ≠  0)(q\;{\neq}\;0)(q=0) is studied.