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

A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests

The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive axiomatics of the space-time geometry that uses light rays and freely falling particles with high velocity, is replaced by several constructions with low velocity particles only. For that purpose we describe in a space-time with a conformal structure and an arbitrary path structure the radial acceleration, a Coriolis acceleration and the zig-zag construction. Each of these quantities give effects whose requirement to vanish can be taken as alternative version of the compatibility axiom of EPS. The procedural advantage lies in the fact, that one can make null-experiments and that one only needs low velocity particles to test the compatibility axiom. We show in addition that Perlick's standard clock can exist in a Weyl space only.Comment: to appear in Gen.Rel.Gra

Understanding quantization: a hidden variable model

We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by stochastically-parameterized c-numbers. Unlike canonical quantization, the method is free from operator ordering ambiguity and the resulting quantum system has a straightforward interpretation as statistical modification of ensemble of classical trajectories. We then develop measurement without wave function collapse \`a la pilot-wave theory and point out new testable predictions.Comment: 16 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz von Foerster Conference 2011)", see http://iopscience.iop.org/1742-6596/361/

E/Z reversible photoisomerization of methyl orange doped polyacrylic acid-based polyelectrolyte brush films

The photoswitching behavior of the polyacrylic acid (PAA) doped by methyl orange (MO) brush film was investigated using spectral analysis of UV-Vis absorbance, Fourier Transformation Infrared spectroscopy, 2D electrical conductivity mapping and Atomic Force Microscopy. The kinetics and time evolution of the photoisomerization of the PAA-MO PEBs film from E-state to Z-state by UV-light irradiation, and reverse thermal relaxation to E-state was explored. The results confirm that the photoisomerization kinetics of the overall peak is the superposition of the photoisomerization kinetics of (Formula presented.) transition, low- and high-frequency of the (Formula presented.) transition bands. The E–Z transformation led to transforming the azobenzene from flat with no dipole moment to 3.0 D dipole moment. Hence, the electrical conductivity escalated accordingly. The transformation of E-state to Z-state led to the collapse of the formed brushes because of the angular rotational momentum consequent to E–Z isomerization

The Dirac-Nambu-Goto p-Branes as Particular Solutions to a Generalized, Unconstrained Theory

The theory of the usual, constrained p-branes is embedded into a larger theory in which there is no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to membranes of arbitrary dimension. For this purpose the tensor calculus in the infinite dimensional membrane space M is developed and an action which is covariant under reparametrizations in M is proposed. The canonical and Hamiltonian formalism is elaborated in detail. The quantization appears to be straightforward and elegant. No problem with unitarity arises. The conventional p-brane states are particular stationary solutions to the functional Schroedinger equation which describes the evolution of a membrane's state with respect to the invariant evolution parameter tau. A tau-dependent solution which corresponds to the wave packet of a null p-brane is found. It is also shown that states of a lower dimensional membrane can be considered as particular states of a higher dimensional membrane.Comment: 28 page

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