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Coherent states in mathematical physics
About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.
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TL;DR: In this paper, the creation and annihilation operators of phase-difference quanta and some other operators in phase space are constructed and the algebraic properties of these operators and the phase difference properties of two-mode coherent states are discussed.
Abstract: In this letter, we have constructed the creation and annihilation operators of phase-difference quanta and some of other operators in phase space. The algebraic properties of these operators and the phase-difference properties of two-mode coherent states are discussed.
3 citations
TL;DR: The coheret-state method is applied to find the normal form of functions of boson creation and annihilation operators as mentioned in this paper, in addition to simple evaluation of commutation relations as ivell as to proving operator identities of interest in radiation and quantum field theory.
Abstract: The coheret-state method is applied to find the normal form of functions of boson creation and annihilation operators. The method is applicable, in addition, to simple evaluation of commutation relations as ivell as to proving operator identities of interest in radiation and quantum field theory. Examples are given to illustrate the method.
3 citations
TL;DR: In this article, the authors obtained and investigated the regular eigenfunctions of simple differential operators xrdr + 1/dxr + 1, r = 1, 2,..., with the eigenvalues equal to 1.
Abstract: We obtain and investigate the regular eigenfunctions of simple differential operators xr dr + 1/dxr + 1, r = 1, 2, ..., with the eigenvalues equal to 1. With the help of these eigenfunctions, we construct a non-unitary analogue of a boson displacement operator which will be acting on the vacuum. In this way, we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0, |1, ..., |r − 1. These states are squeezed, sub-Poissonian in nature and reminiscent of photon-added states in Agarwal and Tara (1991 Phys. Rev. A 43 492).
3 citations
TL;DR: In this article, the authors consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with a unitary irreducible representation of a (compact) Lie group.
Abstract: We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with a unitary irreducible representation of a (compact) Lie group. We show that necessary and sufficient conditions for the possibility of such a representation can be obtained by combining Clebsch–Gordan theory and the reciprocity theorem associated with induced unitary group representations. Applications to several examples involving SU(2), SU(3), and the Heisenberg–Weyl group are presented, showing that there are simple examples of generalized coherent states which do not meet these conditions. Our results are relevant for phase–space description of quantum mechanics and quantum state reconstruction problems.
3 citations
TL;DR: In this paper, an isomorphism between the space free coherent states and the space of distributions on a p-adic disk is constructed for a system with p degrees of freedom.
Abstract: Free coherent states for a system with p degrees of freedom are defined. An isomorphism between the space free coherent states and the space of distributions on p-adic disk is constructed.
3 citations