An Expansion Term In Hamilton's Equations

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta q)=\dot{\pi}+\Theta\pi,$+ (\delta H_{c})/(\delta \pi)=\dot{q}$, where$\Theta = V^{a}_{.;a}$is the expansion of the vector field. Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. In this case the absolute time is the time associated with the fluid's co-moving vector. As measured by this absolute time the expansion term is present. Similarly in cosmology, each observer has a co-moving vector and Hamilton's equations again have an expansion term. It is necessary to include the expansion term to quantize systems such as the above by the canonical method of replacing Dirac brackets by commutators. Hamilton's equations in this form do not have a corresponding sympletic form. Replacing the expansion by a particle number$N\equiv exp(-\int\Theta d \ta)$and introducing the particle numbers conjugate momentum$\pi^{N}$the standard sympletic form can be recovered with two extra fields N and$\pi^N$. Briefly the possibility of a non-standard sympletic form and the further possibility of there being a non-zero Finsler curvature corresponding to this are looked at.Comment: 10 page

Homogeneous variational problems: a minicourse

A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension $m$. In this minicourse we discuss these problems from a geometric point of view.Comment: This paper is a written-up version of the major part of a minicourse given at the sixth Bilateral Workshop on Differential Geometry and its Applications, held in Ostrava in May 201

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

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

An ELISA-based procedure for assaying proteins in digests of human leukocytes and cell lines, using specifically selected peptides and appropriate antibodies

BACKGROUND: We describe the application of an ELISA-based assay (the Peptidomatrix) that can be used to simultaneously identify and quantitate a number of proteins in biological samples. The biological sample (blood component, biopsy, culture or other) is first lysed to release all the proteins, without any additional separation. The denatured proteins in the sample are then digested in bulk with the desired proteolytic enzyme(s). The peptides in the digest are then assayed by appropriate antibodies, using a competition ELISA protocol. RESULTS: As an example of its use, the present paper applies the Peptidomatrix to the assay of four membrane proteins MDR1 (P-glycoprotein or ABCB1), MRP1 (ABCC1), BCRP/MXR (ABCG2) and the alpha subunit of the Na, K_ATPase (ATP1A1), present in a number of cell lines and in human lymphocytes. We show that we can detect and quantitate these proteins, using a series of peptide-antibody pairs, and that we can differentiate between cell lines or cell preparations that express the target proteins and those that do not. CONCLUSION: We have devised a simple, ELISA-based proteomics assay that enables the quantitation of designated proteins in a cell or tissue sample, and that can be used in any laboratory, with minimal specialized equipment

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 causal structure of spacetime is a parameterized Randers geometry

There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes - the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (time-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page

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