Canonical Noether symmetries and commutativity properties for gauge systems

For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation relations with the evolution operators of Lagrangian and Hamiltonian formalisms. Separate characterizations are given in phase space, in velocity space, and through an evolution operator that links both spaces.Comment: 22 pages; some references updated, an uncited reference deleted, minor style change

Singular lagrangians: some geometric structures along the Legendre map

New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics like the projectability of a vector field to a hamiltonian vector field, the computation of the kernel of the presymplectic form of lagrangian formalism, the construction of the lagrangian dynamical vector fields, and the characterisation of dynamical symmetries.Comment: 27 pages; minor changes, a reference update

Gauge transformations for higher-order lagrangians

Noether's symmetry transformations for higher-order lagrangians are studied. A characterization of these transformations is presented, which is useful to find gauge transformations for higher-order singular lagrangians. The case of second-order lagrangians is studied in detail. Some examples that illustrate our results are given; in particular, for the lagrangian of a relativistic particle with curvature, lagrangian gauge transformations are obtained, though there are no hamiltonian gauge generators for them.Comment: 22 pages, LaTe

Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples

Morfoestructura y evolución del ramal N160 de la dorsal de la Cuenca Nor-Fidjiana (Pacífico sudoeste)

The North Fiji Basin is a complex marginal basin formed 10 Ma ago. It is located in the south-west Pacific, on the border of the Pacific and Indo-Australian crustal plates, between two subduction zones of opposed polarity: the New Hebndes trench, to the west, and the Tonga- Kennadec trench, to the east. The North Fiji Basin contains, on a small scale, many of the essential components of global plate tectonics: fracture zones, active spreading ridges, and triple junctions. In the center of the North Fiji Basin, there is a spreading axis constituted of three separate branches which can be individualized in accordance to their dominant directions. One of them, the N160 segment, is discussed in detail in this article, mainly based on recent data sets obtained during the Yokosuka 90 cruise (STARMER project, managed by the IFREMER, France, and the Science and Technology Agency, Japan). The aim of this cruise, carried out between 10th January and 6th February 1991, was the geological and geophysical study of the N160 section of the North Fiji Basin Ridge. Specific features of the N160 segment are pointed out which make it especially interesting with regard to the general knowledge and hypotheses about oceanic spreading ridges. As an example, the N160 segment shows an intermediate spreading rate of 5 cm/a and, at the same time, has a morphology which should be considered as being typical of slow-spreading centers. A succession of en échelon alternating rises and grabens exists between the two triple junctions limiting the segment, the northern one belonging to the Ridge-Ridge-Ridge (RRR) type, and the southern one to the Ridge-Ridge-Fracture Zone (RRF) type. The entire N160 segment is an extremely young morphostructural feature which, according to recorded magnetic stripes, began to be active less than one million years ago as a result of a rapid volcano-tectonic event

Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.Comment: 12 pages, no figures; REVTeX; uses multicol,fancyheadings,eqsecnum; to appear in Phys. Rev.