Some basic properties of infinite dimensional Hamiltonian systems

We consider some fundamental properties of infinite dimensional Hamiltonian systems, both linear and nonlinear. For exemple, in the case of linear systems, we prove a symplectic version of the teorem of M. Stone. In the general case we establish conservation of energy and the moment function for system with symmetry. (The moment function was introduced by B. Kostant and J .M. Souriau). For infinite dimensional systems these conservation laws are more delicate than those for finite dimensional systems because we are dealing with partial as opposed to ordinary differential equations

Quantum Canonical Transformations revisited

A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.Comment: 8 pages, LaTe

On the Groenewold-Van Hove problem for R^{2n}

We discuss the Groenewold-Van Hove problem for R^{2n}, and completely solve it when n = 1. We rigorously show that there exists an obstruction to quantizing the Poisson algebra of polynomials on R^{2n}, thereby filling a gap in Groenewold's original proof without introducing extra hypotheses. Moreover, when n = 1 we determine the largest Lie subalgebras of polynomials which can be unambiguously quantized, and explicitly construct all their possible quantizations.Comment: 15 pages, Latex. Error in the proof of Prop. 3 corrected; minor rewritin

Recent revisions to corporate profits: what we know and when we knew it

Initial estimates in the National Income and Product Accounts significantly overstated U.S. corporate profits for the 1998-2000 period. Subsequent revisions reveal that the profitability of the nation's corporate sector in the late 1990s was substantially weaker than "real-time" data indicated. An unexpected surge in employee stock options exercised-and perhaps, in some sectors, firms' inflated statements of profit-may help explain the large downward revisions.Corporate profits ; Stock options ; Statistics ; Economic indicators

The Effect of Retinoids on the Regenerating Axolotl Spinal Cord

In order to further elucidate the mechanics of the retinoid pathway on Urodele spinal cord regeneration, we employed Antibody/Horseradish Peroxidase Staining of both intact and regenerating Axolotl spinal cord tissues obtained from adult and juvenile animals to determine expression of two retinoid pathway components: Cellular Retinoic Acid Binding Protein II (CRABP II) and Cellular Retinol Binding Protein I (CRBP I). Current results demonstrate that CRABP II is heavily expressed in the arachnoid mater meningeal layer; CRPB I, however, is expressed in the following locations: the pia mater meningeal layer, the nuclei and cytoplasm of gray matter neuroblasts, as well as processes derived from neuroblasts and ependyma. Moreover, the morphogenic nature of the retinoids may possess a significant role in the regeneration-permissive interaction of the meninges and ependyma of the Axolotl spinal cord

Sufficient conditions for the anti-Zeno effect

The ideal anti-Zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system. We present a straightforward way to derive sufficient conditions under which such a situation occurs expressed in terms of the decaying states and spectral properties of the Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno effects is in fact very narrow.Comment: LatEx2e, 9 pages; a revised text, to appear in J. Phys. A: Math. Ge

On continuity and smoothness of group actions

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Dynamics and Lax-Phillips scattering for generalized Lamb models

This paper treats the dynamics and scattering of a model of coupled oscillating systems, a finite dimensional one and a wave field on the half line. The coupling is realized producing the family of selfadjoint extensions of the suitably restricted self-adjoint operator describing the uncoupled dynamics. The spectral theory of the family is studied and the associated quadratic forms constructed. The dynamics turns out to be Hamiltonian and the Hamiltonian is described, including the case in which the finite dimensional systems comprises nonlinear oscillators; in this case the dynamics is shown to exist as well. In the linear case the system is equivalent, on a dense subspace, to a wave equation on the half line with higher order boundary conditions, described by a differential polynomial $p(\partial_x)$ explicitely related to the model parameters. In terms of such structure the Lax-Phillips scattering of the system is studied. In particular we determine the incoming and outgoing translation representations, the scattering operator, which turns out to be unitarily equivalent to the multiplication operator given by the rational function $-p(i\kappa)^*/p(i\kappa)$, and the Lax-Phillips semigroup, which describes the evolution of the states which are neither incoming in the past nor outgoing in the future

Geometrical Description of Quantum Mechanics - Transformations and Dynamics

In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the study of separability and entanglement for states of composite quantum systems.Comment: 22 pages, to be published in Physica Script

Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website http://www.mech.kochi-tech.ac.jp/cheon