The Hamilton-Jacobi Formalism for Higher Order Field Theories

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.Comment: 25 page

Labor outcome among obese postdate women undergoing labor induction

Background: Maternal obesity and postdate pregnancy are common findings among pregnant women worldwide. We aimed to evaluate the influence of maternal obesity on the outcome of labor induction for postdate pregnant women.Methods: We conducted a prospective observational study to compare 118 obese women (≥30 kg/m2) with 118 non-obese women (<30 kg/m2) undergoing labor induction for postdate pregnancy (≥41 weeks). We induced all participants by a uniform protocol according to the Bishop score. The primary outcome measures were the cesarean delivery (CD) rate and the rate of failed induction. Secondary outcomes included prolonged induction- delivery time, prolonged first and second stage of labor, and rate of instrumental delivery. We performed a multivariate regression model to assess for the relation between obesity and the study outcomes of interest.Results: Cesarean delivery was significantly higher in obese women when compared with non-obese women (25.4% vs. 12.7%, p=0.02). Likewise, failed induction rate was significantly lower among non-obese women (5.1% vs. 14.4%. p=0.026). Obese women had increased odds for CD (adjusted odds ratio: 2.24; 95% confidence-interval: 1.13-4.33), failed induction rate (adjusted OR 2.96; 95% CI: 1.15-8.17), prolonged induction-delivery time (adjusted OR 4.57; 95% CI: 1.42-14.74), prolonged first stage of labor (adjusted OR 3.32; 95% CI: 1.07-9.89), prolonged second stage of labor (adjusted OR 4.21; 95% CI: 1.27-13.62), and rate of instrumental delivery (adjusted OR 2.97; 95% CI: 1.16-8.23).Conclusions: Obesity adds more risk to postdate women undergoing induction of labor. Obesity increases the incidence of CD and failed induction among induced postdate women. Therefore, obstetricians should encourage obese women to reduce weight before getting pregnant, and to comply with the optimal weight gain during pregnancy in attempt to reduce the rates of postdating, CD and failed induction

Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation

By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained for a gauge field and a fermion field. For a topologically massive gauge theory, we can obtain a first order Lagrangian with mass term. For the fermion field, in order to make our approach feasible, we supplement the conventional Lagrangian with a surface term. This surface term can also produce the massive term for the fermion.Comment: 30 pages, no figures, v2: discussions and references added, published version matche

Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators

We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms and the gauge transformations and can be used to induce a new theory of gravitation. It can be viewed as a matrix generalization of Einstein general relativity that reproduces the standard Einstein theory in the weak deformation limit. Relations with various mathematical constructions such as Finsler geometry and Hodge-de Rham theory are discussed.Comment: Version accepted by J. High Energy Phys. Introduction and Discussion significantly expanded. References added and updated. (41 pages, LaTeX: JHEP3 class, no figures

Weak Energy: Form and Function

The equation of motion for a time-independent weak value of a quantum mechanical observable contains a complex valued energy factor - the weak energy of evolution. This quantity is defined by the dynamics of the pre-selected and post-selected states which specify the observable's weak value. It is shown that this energy: (i) is manifested as dynamical and geometric phases that govern the evolution of the weak value during the measurement process; (ii) satisfies the Euler-Lagrange equations when expressed in terms of Pancharatnam (P) phase and Fubini-Study (FS) metric distance; (iii) provides for a PFS stationary action principle for quantum state evolution; (iv) time translates correlation amplitudes; (v) generalizes the temporal persistence of state normalization; and (vi) obeys a time-energy uncertainty relation. A similar complex valued quantity - the pointed weak energy of an evolving state - is also defined and several of its properties in PFS-coordinates are discussed. It is shown that the imaginary part of the pointed weak energy governs the state's survival probability and its real part is - to within a sign - the Mukunda-Simon geometric phase for arbitrary evolutions or the Aharonov-Anandan (AA) phase for cyclic evolutions. Pointed weak energy gauge transformations and the PFS 1-form are discussed and the relationship between the PFS 1-form and the AA connection 1-form is established.Comment: To appear in "Quantum Theory: A Two-Time Success Story"; Yakir Aharonov Festschrif

Invariant and polynomial identities for higher rank matrices

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order $d$, where $d$ is the dimension of the matrix. The characteristic polynomials and the Cayley--Hamilton theorem for higher rank matrices are obtained there from

Multi-transmission-line-beam interactive system

We construct here a Lagrangian field formulation for a system consisting of an electron beam interacting with a slow-wave structure modeled by a possibly non-uniform multiple transmission line (MTL). In the case of a single line we recover the linear model of a traveling wave tube (TWT) due to J.R. Pierce. Since a properly chosen MTL can approximate a real waveguide structure with any desired accuracy, the proposed model can be used in particular for design optimization. Furthermore, the Lagrangian formulation provides for: (i) a clear identification of the mathematical source of amplification, (ii) exact expressions for the conserved energy and its flux distributions obtained from the Noether theorem. In the case of uniform MTLs we carry out an exhaustive analysis of eigenmodes and find sharp conditions on the parameters of the system to provide for amplifying regimes

The Higgs mechanism in Finsler spacetimes

Finsler geometry has been recently re-discovered as an interesting possibility to describe spacetime geometry beyond Riemannian geometry. The most evident effect of this class of models is the prediction of modified dispersion relations for particles moving in such backgrounds. In this paper, we are going to consider the effects of modified dispersion relations on a gauge field theory with spontaneous symmetry breaking (SSB) associated to a Higgs field. The percolation of higher dimensional, Lorentz violating operators to lower dimensional ones is discussed. We also discuss the issue of SSB in a mono-metric Finsler scenario like the one associated to the so-called very special relativity.Comment: 11 pages, revtex