Experimental observation of the B(3) field: A reply to Raja et alia

The recent claims by Rajaet al. [1,2] are corrected in this reply. It is shown that there is no Faraday induction due toB ⁽³⁾in vacuo, as observed by these authors. The observation of the inverse Faraday effect by these authors is an observation of theB ⁽³⁾field at second order. Their data, correctly interpreted, constitute strong support for the existence and predicted properties of theB ⁽³⁾field.     

The B(3) field: Its role in the Rayleigh-Jeans law,Planck law,and Einstein coefficients

The role of the novel longitudinal vacuum fieldB ⁽³⁾is discussed in relation to fundamental radiation laws: the Rayleigh-Jeans law, the Planck law, and the Einstein coefficients. The circular index (3) ofB ⁽³⁾causes electromagnetic energy density to be redistributed from the other indices (1) and (2) of the circular basis, but the presence ofB ⁽³⁾in the vacuum does not change the value of the Planck constant h. TheB ⁽³⁾field does not affect, furthermore, the understanding of quantized radiation absorption first proposed by Einstein. Therefore, the experimental observableB ⁽³⁾ does not imply modification of these fundamental, radiation laws, and experimental isolation ofB ⁽³⁾ must take place through its characteristic square root power density dependence when used to magnetize an électron plasma.     

Magnetization of an electron plasma by microwave pulses: Faraday induction

It has been argued theoretically that the recently proposed vacuum fieldB ⁽³⁾ is not accompanied by a real electric fieldE ⁽³⁾ . Experimental evidence for this interence is available in the data reported by Deschampset al. [10], using microwave magnetization of an electron plasma set up in helium gas. Faraday induction due toB ⁽³⁾ does not occur in the inert gas and is not observed experimentally in the absence of free electrons. WheneverB ⁽³⁾ interacts with free electrons, however, Faraday induction occurs through a pulse of induced magnetization (i.e., induced orbital electronic angular momentum).     

The connection between photon mass andB (3) : The poincaré group

The longitudinal vacuum fieldB ⁽³⁾ is an experimental observable which produces by magnetization a well-defined square-root beam power density dependence. Its longitudinal polarization implies that the helicities of the photon are +1, 0, and –1, and that the little group of the Poincaré group is the rotation group 0(3) of a massive boson. The mass of the photon (m) is therefore related directly toB ⁽³⁾ through the Proca equation, and it is concluded that experimental evidence forB ⁽³⁾ is also evidence for finitem.     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.     

Synthesis,Characterization, DNA Binding Properties,Fluorescence Studies and Toxic Activity of Cobalt(III) and Ruthenium(II) Polypyridyl Complexes

The new ligand 4-(isopropylbenzaldehyde)imidazo[4,5-f ][1,10]phenanthroline (ippip) and its complexes [Ru(phen)₂(ippip)]²⁺(1),[Co(phen)₂(ippip)]³⁺(2),[Ru(bpy)₂(ippip)]²⁺(3),[Co(bpy)₂(ippip)]³⁺(4)(bpy=2,2-bipyridine) and (phen=1,10-phenanthroline) were synthesized and characterized by ES⁺-MS, ¹H and ¹³C NMR. The DNA binding properties of the four complexes were investigated by different spectrophotometric methods and viscosity measurements. The results suggest that complexes bind to calf thymus DNA (CT-DNA) through intercalation. When irradiated at 365 nm, the complexes promote the photocleavage of pBR322 DNA, and complex 1 cleaves DNA more effectively than 2, 3, 4 complexes under comparable experimental conditions. Furthermore, photocleavage studies reveal that singlet oxygen (¹O₂) plays a significant role in the photocleavage.     

The Representation of Isometric Operators on <Emphasis Type="Italic">C</Emphasis><Superscript>(1)</Superscript>(<Emphasis Type="Italic">X</Emphasis>)

In this paper,we introduce a new norm on C ⁽¹⁾(X), which is induced by a hexagon on R ², and prove that every isometric operator on C ⁽¹⁾(X) can be induced by a homeomorphism of X, where X is a connected subset of R.     

Noether's theorem and the fieldB (3)

It is shown that the longitudinal, magnetic flux density,B ⁽³⁾ , of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB ⁽³⁾ to the canonical energy-momentum tensorT _µv that appears in Einstein's field equations of general relativity. Thus,B ⁽³⁾ provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory.     

Probability diffusion in non-Markhovian,non-Gaussian molecular ensembles: A theoretical analysis and computer simulation

A theoretical generalisation of the Fokker/Planck equation for atomic and molecular diffusion is compared with the results of a molecular dynamics simulation of a triatomic molecule ofC _2v symmetry. The molecular dynamics results are non-Markhovian and non-Gaussian in nature, markedly so in the case of the centre of mass linear velocityV. This may be ascertained by simulating the long-time limit of the three dimensional kinetic energy autocorrelation function <V ²(t)V ²(0)>/<V ²(0)V ²(0)>, which falls well below the theoretical Gaussian value of 3/5. By expressing the Mori continued fraction as a multidimensional Markhovian chain of differential equations and expressing this in turn as a non-Gaussian probability-diffusion equation of the Kramers/Moyal type it is possible to account for the simulation results in a qualitative fashion.     

Derivation of the vacuum longitudinal fieldB (3) from the Dirac equation of the electron in the electromagnetic field

By solving the Diras equation for the motion of an electron (c) in the circularly polarized electromagnetic field it is shown that the intrinsic electron spin forms an interaction Hamiltonian with a time independent fieldB ⁽³⁾ of electromagnetic radiation in the vacuum. In the same way as intrinsic spin is a fundamental property of the electron,B ⁽³⁾ is therefore a fundamental and intrinsic property of the vacuum electromagnetic field.     

Realization of a unique time evolution unitary operator in Klein Gordon theory

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL ²(R ³) and the Einstein’s relativistic equation in the spaceL ²(R ³, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL ²(R ³) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL ²(R ³).     

Determination of the Stereochemistry of Substituted 5-Methylenehydantoins and Thiohydantoins by 13C NMR and Homonuclear NOE Experiments

Basically the aim of this work is to define the accurate configuration of the exocyclic double bond of substituted 5-methylenehydantoins and thiohydantoins which have been conceived as potential Aldose Reductase inhibitors. A previsional survey based upon the chemical shifts analysis from ¹H and decoupled ¹³C NMR spectra discloses, for a part of the family of compounds, the assignment of the Zconfiguration for unsubstituted (2,3) and N-3 substituted (6,7,9) derivatives, and the E-configuration for the N-1 substituted (8,11) ones. The qualitative study with Homonuclear NOE (8,11) and the coupling constant measuring ^{3 J}C4-C=C-H6 from coupled ¹³C NMR (1–11), lead to the assignment of the accurate configuration of the whole family's compounds in agreement with the previsional study.     

Formation of Cs molecules via Feshbach resonances stabilized by spontaneous emission: theoretical treatment with the Fourier grid method

This paper proposes a general method to investigate Feshbach resonances in atomic collisions similar to Cs(6 s ) + Cs(6 p ) in the thermal or cold regime. In order to compute the predissociation widths of the C ¹ Π _u (6 s + 5 d ) bound vibrational levels of Cs₂, coupled both with the (2) ³ Σ ⁺ _u (6 s + 6 p ) continuum and with the (2) ³ Π _u (6 s + 5 d ) vibrational series, a Fourier grid method is implemented, with an optical potential. A convenient way of optimizing the latter is proposed. A large number of resonances are found and calculations of their cross-sections for stabilization into ground state molecules show that the rate may be important. This confirms the interpretation of Lintz and Bouchiat [Phys. Rev. Lett. 80, 2570 (1998)] who observed dimer formation in cell experiments. Possible generalization to the cold regime relies on the possibility to tune the position of a resonance to coincide with the maximum of the collisional energy distribution. Received 14 February 2002 Published online 28 June 2002     

Polarizabilities of rubidium (9-10)S 1/2 and 8D 3/2, 5/2 states

Polarizabilities of several rubidium states were determined by measuring stark shifts of transitions using an electro-optically modulated laser beam to excite an atomic beam. The voltage required for atoms excited by the laser beam in an electric field to be simultaneously in resonance as atoms excited by a frequency sideband of the laser in a field free region was measured. The scalar α and tensor α ₂ polarizabilities were found to be: α (9 S _1/2 ) = 103.77±0.09, α (10 S _1/2 ) = 272.54±0.16, α (8 D _3/2 ) = 230.68±0.25 and α ₂ (8 D _3/2 ) = 26.55±0.10, α (8 D _5/2 ) = 222.68±0.14 and α ₂ (8 D _5/2 ) = 51.91±0.10 MHz/(kV/cm)². The results are 100 times more accurate than previous measurements and are within 1% of those found theoretically using a Coulomb approximation calculation. Received 7 September 2000 and Received in final form 6 December 2000     

On the linearized relativistic Boltzmann equation

The linearized relativistic Boltzmann equation inL ²(r,p) is investigated. The detailed analysis of the collision operatorL is carried out for a wide class of scattering cross sections.L is proved to have a form of the multiplication operatorv(p) plus the compact inL ²(p) perturbationK. The collisional frequencyv(p) is analysed to discriminate between relativistic soft and hard interactions. Finally, the existence and uniqueness of the solution to the linearized relativistic Boltzmann equation is proved.     

Charge Conjugation and the B(3) Field: A Reply to Comay

The argument for non-existence of the B ⁽³⁾ field proposed by E. Comay is based on adding radians to the phase of a plane wave. This is trivially incorrect because B ⁽³⁾ is a vacuum component of a C conserving Yang-Mills gauge field theory.     

Heterodyne coincidence spectroscopy

A new type of light-scattering experiment, which should measure directly the triple static structure factor S ⁽³⁾ (k, q) of a fluid, is proposed. S ⁽³⁾(k, q) is the full spatial Fourier transform of the equilibrium triplet distribution function g ⁽³⁾(r ₁, r ₂, r ₃). The experiment may also be used to study dynamic correlation functions of the form <a_k (t)a_q (t′)a_k_q(t″)> (where a_k () is the kth spatial Fourier component of the density), thereby giving new information on mode-mode coupling. The method obtains its information from triple correlations in the arrival of scattered photons at three detectors. The detectors must be operated in the heterodyne mode (i.e. with a local oscillator); the scattering volume must be much larger than the volume over which molecular positions are correlated. Comparison is made with previous analyses of other multi-detector experiments.     

On the existence of <Emphasis Type="Bold">1, 3</Emphasis>P <Emphasis Type="Bold">o</Emphasis> resonances in H<Superscript>-</Superscript> between n = 2 and 3 H thresholds

We examine the influence of relativistic and QED effects on the existence of the ^1,3P ^o H^- resonances between n = 2 and 3 hydrogen thresholds, the relativistic and QED corrections and the coupling effects between the high singlet and triplet states are considered as first-order perturbations. We firstly obtain accurate non-relativistic resonant energies and widths of fifteen ¹P ^o resonances, and fifteen ³P ^o resonances. The fifteen ¹P ^o resonances are classified to be ₃ (2, 0) ^- _n ( 4 ? n ? 12) and ₃ (1, 1) ⁺ _n ( 3 ? n ? 8). The fifteen ³P ^o resonances are classified to be ₃ (2, 0) ⁺ _n ( 3 ? n ? 12) and ₃ (1, 1) ^- _n ( 4 ? n ? 8). We found there exist six Feshbach resonances for ₃ (2, 0) ^- _n (¹P ^o ) series, four Feshbach resonances for ₃ (1, 1) ⁺ _n (¹P ^o ) series, seven Feshbach resonances for ₃ (2, 0) ⁺ _n (³P ^o ) series, and three Feshbach resonances for ₃ (1, 1) ^- _n (¹P ^o ) series. Received 22 February 2002 Published online 24 September 2002     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

Stark shifts and fine structure of the Li 3 D states

⁶Li 3²D _{3/2, 5/2} states were studied using a diode laser to first excite the 2P _3/2 state and a dye laser to populate the 3²D _{3/2, 5/2} states. The dye laser was modulated by an electro-optic modulator and intersected an atomic beam that passed through a field free region and subsequently through a uniform electric field. A value of 1084.24±0.20 MHz was found for the 3²D fine structure splitting. The scalar and tensor polarizabilities were determined to be α (3D _3/2 ) = - 3.753±0.015, α ₂ (3D _3/2 ) = 2.893±0.017, α (3D _5/2 ) = - 3.772±0.008 and α ₂ (3D _5/2 ) = 4.058±0.013 MHz/(kV/cm)². Received 26 September 2002 / Received in final form 22 January 2003 Published online 11 March 2003 RID="a" ID="a"e-mail: wlaser@yorku.ca