Multi-Lagrangians, Hereditary Operators and Lax Pairs for the Korteweg-de Vries Positive and Negative Hierarchies

We present an approach to the construction of action principles for differential equations, and apply it to field theory in order to construct systematically, for integrable equations which are based on a Nijenhuis (or hereditary) operator, a ladder of action principles which is complementary to the well-known multi-Hamiltonian formulation. We work out results for the Korteweg-de Vries (KdV) equation, which is a member of the positive hierarchy related to a hereditary operator. Three negative hierarchies of (negative) evolution equations are defined naturally from the hereditary operator as well, in the context of field theory. The Euler-Lagrange equations arising from the action principles are equivalent to the original evolution equation + deformations, which are obtained in terms of the positive and negative evolution vectors. We recognize the Liouville, Sinh-Gordon, Hunter-Zheng and Camassa-Holm equations as negative equations. The ladder for KdV is directly mappable to a ladder for any of these negative equations and other positive equations (e.g., the Harry-Dym and a special case of the Krichever-Novikov equations): a new nonlocal action principle for the deformed system Sinh-Gordon + spatial translation vector is presented. Several nonequivalent, nonlocal time-reparametrization invariant action principles for KdV are constructed. Hamiltonian and Symplectic operators are obtained in factorized form. Alternative Lax pairs for all negative flows are constructed, using the flows and the hereditary operator as only input. From this result we prove that all positive and negative equations in the hierarchies share the same sets of local and nonlocal constants of the motion for KdV, which are explicitly obtained using the local and nonlocal action principles for KdV.Comment: Final version, accepted in JMP; RevTeX, 31 page

Test particles behavior in the framework of a lagrangian geometric theory with propagating torsion

Working in the lagrangian framework, we develop a geometric theory in vacuum with propagating torsion; the antisymmetric and trace parts of the torsion tensor, considered as derived from local potential fields, are taken and, using the minimal action principle, their field equations are calculated. Actually these will show themselves to be just equations for propagating waves giving torsion a behavior similar to that of metric which, as known, propagates through gravitational waves. Then we establish a principle of minimal substitution to derive test particles equation of motion, obtaining, as result, that they move along autoparallels. We then calculate the analogous of the geodesic deviation for these trajectories and analyze their behavior in the nonrelativistic limit, showing that the torsion trace potential $\phi$ has a phenomenology which is indistinguishable from that of the gravitational newtonian field; in this way we also give a reason for why there have never been evidence for it.Comment: 12 pages, no figures, to appear on Int. Journ. Mod. Phys.

Consistency of Semiclassical Gravity

We discuss some subtleties which arise in the semiclassical approximation to quantum gravity. We show that integrability conditions prevent the existence of Tomonaga-Schwinger time functions on the space of three-metrics but admit them on superspace. The concept of semiclassical time is carefully examined. We point out that central charges in the matter sector spoil the consistency of the semiclassical approximation unless the full quantum theory of gravity and matter is anomaly-free. We finally discuss consequences of these considerations for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2

Bohmian Mechanics and Quantum Information

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure

Duality properties of Gorringe-Leach equations

In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold-Vassiliev type. The specific associated conserved quantities (Laplace-Runge-Lenz vector and Fradkin-Jauch-Hill tensor) are then dual reflections one of the othe

Spinning particles in Schwarzschild-de Sitter space-time

After considering the reference case of the motion of spinning test bodies in the equatorial plane of the Schwarzschild space-time, we generalize the results to the case of the motion of a spinning particle in the equatorial plane of the Schwarzschild-de Sitter space-time. Specifically, we obtain the loci of turning points of the particle in this plane. We show that the cosmological constant affect the particle motion when the particle distance from the black hole is of the order of the inverse square root of the cosmological constant.Comment: 8 pages, 5 eps figures, submitted to Gen.Rel.Gra

The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics

We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of this approach are briefly summarized.Comment: 21 pages, 6 figures. Contribution to E. Seiler and I.-O. Stamatescu (editors): `Approaches To Fundamental Physics -- An Assessment Of Current Theoretical Ideas' (Springer Verlag, to appear

Torsion-induced spin precession

We investigate the motion of a spinning test particle in a spatially-flat FRW-type space-time in the framework of the Einstein-Cartan theory. The space-time has a torsion arising from a spinning fluid filling the space-time. We show that for spinning particles with nonzero transverse spin components, the torsion induces a precession of particle spin around the direction of the fluid spin. We also show that a charged spinning particle moving in a torsion-less spatially-flat FRW space-time in the presence of a uniform magnetic field undergoes a precession of a different character.Comment: latex, 4 eps figure

High-spin states and band terminations in v 49

High-spin states in 49 V have been studied through the 28 Si(28 Si, α3p) reaction using the EUROBALL γ-ray detector array. The 49 V level scheme has been extended up to 13.1 MeV including 21 new states. Both negative and positive parity states have been interpreted in the framework of theShell Model. The 27/2− and the 31/2+ band termination states have been observed in agreement with theoretical predictions.Fil: Rodrigues Ferreira Maltez, Dario Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia Física (Centro Atómico Constituyentes). Proyecto Tandar; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Hojman, Daniel Leonardo. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia Física (Centro Atómico Constituyentes). Proyecto Tandar; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lenzi, Silvia M.. Istituto Nazionale Di Fisica Nucleare.; Italia. Università di Padova; ItaliaFil: Cardona, Maria Angelica. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia Física (Centro Atómico Constituyentes). Proyecto Tandar; Argentina. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; ArgentinaFil: Fernea, Enrico. Università di Padova; Italia. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Axiotis, M.. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Beck, C.. Université de Strasbourg; Francia. Centre National de la Recherche Scientifique; FranciaFil: Bednarczyk, P.. Polish Academy of Sciences; ArgentinaFil: Bizzetti, P. G.. Università di Padova; Italia. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Bizzetti Sona, A. M.. Università di Padova; Italia. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Della Vedova, F.. Università di Padova; Italia. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Grebosz, J.. Polish Academy of Sciences; ArgentinaFil: Haas, F.. Université de Strasbourg; Francia. Centre National de la Recherche Scientifique; FranciaFil: Kmiecik, M.. Polish Academy of Sciences; ArgentinaFil: Maj, A.. Polish Academy of Sciences; ArgentinaFil: Męczyński, W.. Polish Academy of Sciences; ArgentinaFil: Napoli, D. R.. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Nespolo, M.. Università di Padova; Italia. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Papka, P.. Université de Strasbourg; Francia. Centre National de la Recherche Scientifique; FranciaFil: Sánchez i Zafra, A.. Université de Strasbourg; Francia. Centre National de la Recherche Scientifique; FranciaFil: Styczen, J.. Polish Academy of Sciences; ArgentinaFil: Thummerer, S.. Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und Meeresforschung; AlemaniaFil: Ziębliński, M.. Polish Academy of Sciences; Argentin