On the symplectic two-form of gravity in terms of Dirac eigenvalues

The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework. (C) 2002 Published by Elsevier B.V. B.V.

Local physical coordinates from symplectic projector method

The basic arguments underlying the symplectic. projector method are presented. By this method, local free coordinates on the constraint surface can be obtained for a broader class of constrained systems. Some interesting examples are analyzed.

Construction of time-dependent dynamical invariants: A new approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Partial hyperbolicity for symplectic diffeomorphisms

We prove that every robustly transitive and every stably ergodic symplectic diffeomorphism on a compact manifold admits a dominated splitting. In fact, these diffeomorphisms are partially hyperbolic. (c) 2005 Elsevier SAS. All rights reserved.

Symplectic actions on coadjoint orbits

We present a compact expression for the field theoretical actions based on the symplectic analysis of coadjoint orbits of Lie groups. The final formula for the action density α c becomes a bilinear form 〈(S, 1/λ), (y, m y)〉, where S is a 1-cocycle of the Lie group (a schwarzian type of derivative in conformai case), λ is a coefficient of the central element of the algebra and script Y sign ≡ (y, m y) is the generalized Maurer-Cartan form. In this way the action is fully determined in terms of the basic group theoretical objects. This result is illustrated on a number of examples, including the superconformal model with N = 2. In this case the method is applied to derive the N = 2 superspace generalization of the D=2 Polyakov (super-) gravity action in a manifest (2, 0) supersymmetric form. As a byproduct we also find a natural (2, 0) superspace generalization of the Beltrami equations for the (2, 0) supersymmetric world-sheet metric describing the transition from the conformal to the chiral gauge.

Symplectic bosons, Fermi fields and super Jordan algebras

A construction relating the structures of super Lie and super Jordan algebras is proposed. This may clarify the role played by field theoretical realizations of super Jordan algebras in constructing representations of super Kač-Moody algebras. The case of OSP(m, n) and super Clifford algebras involving independent Fermi fields and symplectic bosons is discussed in detail.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Darboux invariants for planar polynomial differential systems having an invariant conic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the global dynamics of the Rabinovich system

In this paper by using the Poincare compactification in R(3) make a global analysis of the Rabinovich system(x) over dot = hy - v(1)x + yz, (y) over dot = hx - v(2)y - xz, (z) over dot = -v(3)z + xy,with (x, y, z) is an element of R(3) and ( h, v(1), v(2), v(3)) is an element of R(4). We give the complete description of its dynamics on the sphere at infinity. For ten sets of the parameter values the system has either first integrals or invariants. For these ten sets we provide the global phase portrait of the Rabinovich system in the Poincare ball (i.e. in the compactification of R(3) with the sphere S(2) of the infinity). We prove that for convenient values of the parameters the system has two families of singularly degenerate heteroclinic cycles. Then changing slightly the parameters we numerically found a four wings butterfly shaped strange attractor.

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

First-order actions: A new view

We analyse systems described by first-order actions using the Hamilton-Jacobi (HJ) formalism for singular systems. In this study we verify that generalized brackets appear in a natural way in HJ approach, showing us the existence of a symplectic structure in the phase space of this formalism.

CP violation conditions in N-Higgs-doublet potentials

Conditions for CP violation in the scalar potential sector of general N-Higgs-doublet models are analyzed from a group theoretical perspective. For the simplest two-Higgs-doublet model potential, a minimum set of conditions for explicit and spontaneous CP violation is presented. The conditions can be given a clear geometrical interpretation in terms of quantities in the adjoint representation of the basis transformation group for the two doublets. Such conditions depend on CP-odd pseudoscalar invariants. When the potential is CP invariant, the explicit procedure to reach the real CP-basis and the explicit CP transformation can also be obtained. The procedure to find the real basis and the conditions for CP violation are then extended to general N-Higgs-doublet model potentials. The analysis becomes more involved and only a formal procedure to reach the real basis is found. Necessary conditions for CP invariance can still be formulated in terms of group invariants: the CP-odd generalized pseudoscalars. The problem can be completely solved for three Higgs-doublets.

The Faddeev-Jackiw approach and the conformal affine sl(2) Toda model coupled to the matter field

The conformal affine sl(2) Toda model coupled to the matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and gauge fixing the conformal symmetry. (C) 2000 Academic Press.

Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences

We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine sl(3)((1)) Toda model coupled to matter fields. The theory is treated as a constrained system in the context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The sl(n)((1)) case is also outlined. (C) 2002 American Institute of Physics.

On equivalence of Duffin-Kemmer-Petiau and Klein-Gordon equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)