Routh reduction for singular Lagrangians

This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian $L$ or the momentum map $J_L$ are required apart from the momentum being a regular value of $J_L$. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler-Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and interpretation of the Euler-Lagrange equations for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric.Comment: 34 pages, 2 figures, accepted for publicaton in International Journal of Geometric Methods in Modern Physics (IJGMMP

Ethnic differential item functioning in the assessment of quality of life in cancer patients

BACKGROUND: Past research has shown that Filipino cancer patients report lower levels of quality of life (QoL) than other ethnic groups. One possible explanation for this is that Filipinos do not define QoL in the same manner as others, resulting in bias in their assessments. Hence, Filipinos would not necessarily have lower QoL. METHODS: Item response theory methods were used to assess differential item functioning (DIF) in the quality of life (measured by the EORTC QLQ-C30) of cancer patients across four ethnic groups (Caucasian, Filipino, Hawaiian, and Japanese). The sample consisted of 359 cancer patients. RESULTS: Results showed the presence of DIF on several items, indicating ethnic differences in the assessment of quality of life. Relative to the Caucasian and Japanese groups, items related to physical functioning, cognitive functioning, social functioning, nausea and vomiting, and financial difficulties exhibited DIF for Filipinos. On these items Filipinos exhibited either higher or lower QoL scores, even though their overall QoL was the same. CONCLUSION: This evidence may explain why Filipinos have previously been found to have lower overall QoL. Although Filipinos score lower on QoL than other groups, this may not reflect lower QoL, but rather differences in how QoL is defined. The presence of DIF did not appear, however, to alter the psychometric properties of the QLQ-C30

The Tulczyjew triple for classical fields

The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important feature of our approach is that we do not postulate {\it ad hoc} the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of Field Theory is covariant and complete, containing not only the Lagrangian formalism and Euler-Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps $\alpha$ and $\beta$ which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We discuss also the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theor

Quantum cosmological perfect fluid model and its classical analogue

The quantization of gravity coupled to a perfect fluid model leads to a Schr\"odinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = \alpha\rho$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of $\alpha$, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.Comment: Latex file, 13 page

Differential geometry, Palatini gravity and reduction

The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the frame bundle $LM$ are used. A generalization of Lagrange-Poincar\'e reduction scheme to these types of variational problems allows us to relate it with the Einstein-Hilbert variational problem. Relations with some other variational problems for gravity found in the literature are discussed.Comment: 28 pages, no figures. (v3) Remarks, discussion and references adde

Codimension one symplectic foliations and regular Poisson structures

Original manuscript June 21, 2011In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in [9]

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