Nonrelativistic Geodesic Motion

We show that any second-order dynamic equationon a configuration space X R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.     

Nonequivalent Representations of Nuclear Algebras of Canonical Commutation Relations: Quantum Fields

Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in nonequivalent quantizations of scalar fields.     

Translation Gauge Fields and Space-Time Dislocations

Gauge fields of Poincaré translations define particular nongravitation structure on a space-time, which can be treated as sui generis space-time dislocations. Their source is the canonical energy-momentum tensor of matter, and these dislocations can introduce some corrections to standard values of gravitation effects, e. g. the Yukawa type corrections to the Newtonian gravitation potential.     

Gravity as a goldstone field in the Lorentz gauge theory

A bundle formalism is applied to interpret the Einstein gravitational field in gauge theory; its topological invariants are discussed.     

Systematic investigations of anthocyanin–metal interactions by Raman spectroscopy

The FT‐Raman spectra of the chloride salts of pelargonidin‐3‐glucoside, cyanidin‐3‐glucoside and delphinidin‐3‐glucoside, their structures at pH 5.0 and their interaction with aluminium and ferric ions are presented for the first time and discussed with regard to their spectroscopic response. Two marker bands at approximately 1510 and 1330/1350 cm⁻¹ and one band at approximately 1330/1350 cm⁻¹ were identified being characteristic for the formation of ferric and aluminium chelates, respectively, of cyanidin‐3‐glucoside and delphinidin‐3‐glucoside. In contrast, pelargonidin‐3‐glucoside, exhibiting one single hydroxyl group in the B‐ring, did not form metal chelates, which could be clearly demonstrated by missing marker bands. The formation of anthocyanin–metal chelates was also verified in model systems containing commercial sugar beet pectin and a pectic polysaccharide fraction isolated thereof, respectively. In addition, the absence of anthocyanin–metal chelates in systems prepared with citrate buffer was confirmed, and the effects of low and high methoxylated citrus pectins on chelate formation were studied. Copyright © 2012 John Wiley & Sons, Ltd.     

Residual {\bar\partial}-cohomology and the complex Radon transform on subvarieties of {\mathbb C P^n}

We show that the complex Radon transform realizes an isomorphism between the quotient-space of residual ${\bar\partial}$ -cohomologies of a locally complete intersection algebraic subvariety in a linearly concave domain of ${{{\mathbb C}}P^n}$ and the space of holomorphic solutions of the associated homogeneous system of differential equations with constant coefficients in the dual domain in ${({{\mathbb C}}P^n)^*}$ .     

Reactions of polystyryllithiums and model lithium carbanions with 9,10‐bis(halomethyl)anthracenes

The direct and nearly quantitative incorporation of 9,10‐anthracenylidene (AN) chromophores into polystyrene occurred via the reaction of polystyryllithium (PSLi) with 9,10‐bis(chloromethyl)anthracene (BCMA) at ?78 °C in tetrahydrofuran (THF)/ hexane containing between 30 and 40 vol % hexane. Although the reaction of PSLi and BCMA or 9,10‐bis(bromomethyl)anthracene (BBMA) in THF at ?78 °C gave nearly quantitative coupling, typically only 30–50% AN incorporation was observed, as determined by ultraviolet–visible spectrometry. Model coupling reactions of 3,3‐dimethyl‐1,1‐diphenyl‐1‐lithiobutane, (1,1,2,2‐tetramethyl)propylcyclopentadienyllithium, 9‐methylfluorenyllithium, and triphenylmethyllithium with BCMA or BBMA at ?78 °C in THF in nearly all cases gave several AN‐containing coupling products. This was consistent with lithium–halogen exchange leading to the linking of multiple AN groups. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3121–3129, 2001     

On the Higgs feature of gravity

The gauge gravitation theory, based on the equivalence principle besides the gauge principle, is formulated in the fibre bundle terms. The correlation between gauge geometry on spinor bundles describing Dirac fermion fields and space-time geometry on a tangent bundle is investigated. We show that field functions of fermion fields in presence of different gravitational fields are always written with respect to different reference frames. Therefore, the conventional quantization procedure is applicable to fermion fields only if gravitational field is fixed. Quantum gravitational fields violate the above mentioned correlation between two geometries.     

Covariant Hamiltonian Field Theory: Path Integral Quantization

The Hamiltonian counterpart of classical Lagrangian field theory is covariant Hamiltonian field theory where momenta correspond to derivatives of fields with respect to all world coordinates. In particular, classical Lagrangian and covariant Hamiltonian field theories are equivalent in the case of a hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is almost-regular. In order to quantize covariant Hamiltonian field theory, one usually attempts to construct and quantize a multisymplectic generalization of the Poisson bracket. In the present work, the path integral quantization of covariant Hamiltonian field theory is suggested. We use the fact that a covariant Hamiltonian field system is equivalent to a certain Lagrangian system on a phase space which is quantized in the framework of perturbative quantum field theory. We show that, in the case of almost-regular quadratic Lagrangians, path integral quantizations of associated Lagrangian and Hamiltonian field systems are equivalent.