Tri-hamiltonian vector fields, spectral curves and separation coordinates

We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to its symplectic leaves. The frameworks is applied to Lax equations with spectral parameter, for which not only it unifies the separation techniques of Sklyanin and of Magri, but also provides a more efficient ``inverse'' procedure not involving the extraction of roots.Comment: 49 pages Section on reduction revisite

Nonlinear massive spin-two field generated by higher derivative gravity

We present a systematic exposition of the Lagrangian field theory for the massive spin-two field generated in higher-derivative gravity. It has been noticed by various authors that this nonlinear field overcomes the well known inconsistency of the theory for a linear massive spin-two field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called "(Helmholtz-)Jordan frame" and "Einstein frame". In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-two field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame. The full equations of motion and the energy-momentum tensor for the spin--two field in Einstein frame are given, and a simple but nontrivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-two field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-two field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected

The Universality of Einstein Equations

It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as independent variables, leads to ``universal'' equations. If the dimension $n$ of space--time is greater than two these universal equations are Einstein equations for a generic Lagrangian and are suitably replaced by other universal equations at bifurcation points. We show that bifurcations take place in particular for conformally invariant Lagrangians $L=R^{n/2} \sqrt g$ and prove that their solutions are conformally equivalent to solutions of Einstein equations. For 2--dimensional space--time we find instead that the universal equation is always the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the Levi--Civita connection of the metric and an additional vectorfield ensuing from conformal invariance. As an example, we investigate in detail some polynomial Lagrangians and discuss their bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9

Non-Trivial Vacua in Higher-Derivative Gravitation

A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory. It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.Comment: 25 pages, LaTeX2e with AMS-LaTeX 1.2, 7 eps figure

The dynamical equivalence of modified gravity revisited

We revisit the dynamical equivalence between different representations of vacuum modified gravity models in view of Legendre transformations. The equivalence is discussed for both bulk and boundary space, by including in our analysis the relevant Gibbons-Hawking terms. In the f(R) case, the Legendre transformed action coincides with the usual Einstein frame one. We then re-express the R+f(G) action, where G is the Gauss-Bonnet term, as a second order theory with a new set of field variables, four tensor fields and one scalar and study its dynamics. For completeness, we also calculate the conformal transformation of the full Jordan frame R+f(G) action. All the appropriate Gibbons-Hawking terms are calculated explicitly.Comment: 17 pages; v3: Revised version. New comments added in Sections 3 & 5. New results added in Section 6. Version to appear in Class. Quantum Gravit

Ostrogradski Formalism for Higher-Derivative Scalar Field Theories

We carry out the extension of the Ostrogradski method to relativistic field theories. Higher-derivative Lagrangians reduce to second differential-order with one explicit independent field for each degree of freedom. We consider a higher-derivative relativistic theory of a scalar field and validate a powerful order-reducing covariant procedure by a rigorous phase-space analysis. The physical and ghost fields appear explicitly. Our results strongly support the formal covariant methods used in higher-derivative gravity.Comment: 22 page

The Role of Emotional Intelligence in Health Care Professionals Burnout

The purpose of this study is to explore the relationship between Emotional Intelligence (EI) and burnout in health care professionals. More specifically, this survey has the purpose of demonstrating the role of EI as a protective factor against the risk of burnout. Health professionals (doctors, nurses, and other caregivers) composed the sample. Data, collected during professional training, provided 148 employees. Major results of this survey underline the relationship between EI and burnout. As we expected, there is a negative and significant correlation between burnout and Emotional Intelligence. Moreover, burnout varies depending on length of service: burnout increases between 5 and 10 years of experience and decreases over 10 years. Indeed, burnout is differently expressed amongst healthcare professionals: more specifically, Psycho-physical exhaustion, Detriment of the relationships and Burnout (total score) has an impact on physician (doctors) more than other investigated health professionals. These findings seem to suggest the opportunity to improve Emotional Intelligence abilities through specific training programs, useful to promote the ability to cope with stress and to enrich the relationships in the workplace

Gauge Fixing in Higher Derivative Gravity

Linearized four-derivative gravity with a general gauge fixing term is considered. By a Legendre transform and a suitable diagonalization procedure it is cast into a second-order equivalent form where the nature of the physical degrees of freedom, the gauge ghosts, the Weyl ghosts, and the intriguing "third ghosts", characteristic to higher-derivative theories, is made explicit. The symmetries of the theory and the structure of the compensating Faddeev-Popov ghost sector exhibit non-trivial peculiarities.Comment: 21 pages, LaTe