Showing papers on "Coherent states in mathematical physics published in 1984"
TL;DR: In this article, the Barut-Girardello representation was reformulated in terms of coherent states by generalizing to Spc(2d,R) coherent states introduced by Barut and Girardello.
Abstract: The present series of papers deals with various realizations of the dynamical group Spc(2d,R) of microscopic collective states for an A nucleon system in d (=1,2, or 3) dimensions, when these collective states are assumed to be invariant under the orthogonal group O(n) associated with the n=A−1 relative Jacobi vectors. In this paper, we further study the Barut–Girardello representation proposed in the first two papers of the present series to show that it may be reformulated in terms of some coherent states by generalizing to Spc(2d,R) a class of Sp(2,R) coherent states introduced by Barut and Girardello. For such purpose, our starting point is another coherent state representation, namely the Perelomov one, previously considered by Kramer. We also propose a third, new class of coherent states leading to Holstein–Primakoff representation in a straightforward way. We review various properties of these three classes of coherent states, such as their reproducing kernel and measure explicit forms, their gener...
54 citations
TL;DR: In this paper, the identity of the Vproportional(z-1/z)/sup 2/ ) coherent states for general potentials is explicitly derived and it is shown that these states are a generalization to arbitrary (noninteger) charge of the charged-boson coherent states.
Abstract: After arguing on intuitive grounds that the minimum-uncertainty coherent states for general potentials are complete, the resolution of the identity for a specific example Vproportional(z-1/z)/sup 2/ is explicitly derived. It is then shown that these states are a generalization to arbitrary (noninteger) charge of the charged-boson coherent states.
18 citations
TL;DR: When the potential is the Fourier transform of a totally finite complex-valued measure, a formula for the one-parameter unitary group generated by the Schrodinger operator in L2 (IRn) is obtained entirely in terms of the basic field operators in a suitable Fock space by means of quantum stochastic calculus.
Abstract: When the potential is the Fourier transform of a totally finite complex-valued measure, a formula for the one-parameter unitary group generated by the Schrodinger operator in L2 (IRn) is obtained entirely in terms of the basic field operators in a suitable Fock space by means of quantum stochastic calculus.
5 citations
TL;DR: In this article, the authors define coherent states with domains in the complex plane by means of ladder operators acting in a separable Hilbert space, and some properties of the states are derived and examples provided to indicate areas of possible applications.
Abstract: Planar coherent states with domains in the complex plane are defined by means of ladder operators acting in a separable Hilbert space. Some properties of the states are derived and examples provided to indicate areas of possible applications.