"Square Root" of the Proca Equation: Spin-3/2 Field Equation

New equations describing particles with spin 3/2 are derived. The non-local equation with the unique mass can be considered as "square root" of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The local equation describes spin 3/2 particles with three mass states. The equations considered involve fields with spin-3/2 and spin-1/2, i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and spin projections are obtained. All independent solutions of the local equation are expressed through projection matrices. The first order relativistic wave equation in the 20-dimensional matrix form, the relativistically invariant bilinear form and the corresponding Lagrangian are given. Two parameters characterizing non-minimal electromagnetic interactions of fermions are introduced, and the quantum-mechanical Hamiltonian is found. It is proved that there is only causal propagation of waves in the approach considered.Comment: 17 pages, corrections in Eqs. (50), (51

Oral Intake of Sardinella Longiceps Oil the Decrease of Tnf-? and Il-6 Levels in Atherosclerotic Wistar Rat

Lifestyle changes to consumption of variegated instant food may be associated several heath hazards, such as obesity, dyslipidemia, and atheroschlerosis. This study was conducted to investigate the effects of orally administered Sardinella longiceps oil as an anti inflammatory agent on the serum levels of TNF-? and IL-6 considered as biomarkers for atherosclerosis.The study design is an true experimental with randomized pretest and posttest control group design, using 50 Wistar rat equaly divided into 5 groups, i.e. placebo control group 0% and 4 treatment groups each treated daily with 10%, 15 %, 20 % and 25 % fish oil respectively for 6 weeks. Before the treatment was started, all rats were orally fed daily with a high cholesterol diet for 13 weeks to induce atherosclerosis. Our study showed that the intake of 20% fish oil had resulted in the significantly greatest decrease of 45,63 % in the TNF-? serum levels,from 28.62 ± 1.25 to 15.56 ± 7.20 ?g/mL and similar significant decrease 15,42% in of IL-6 serum levels from 134.64 ± 1.98 to 113.87 ± 4.30 ?g/mL. The overall results of our study seemed to imply than in the Wistar rats, oral intake of Sardfinella longiceps oils signifacantly decreased serum levels of TNF-? and IL-6 probably through their anti-inflamatory effects. Futher research to determin the magnitude of effects sardinella longiceps oils on the serum levels TNF-? and IL-6 human

Statistical field theories deformed within different calculi

Within framework of basic-deformed and finite-difference calculi, as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis to be generalized by Naudts, we develop field-theoretical schemes of statistically distributed fields. We construct a set of generating functionals and find their connection with corresponding correlators for basic-deformed, finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of additive functionals, whose expansions into deformed series yield both Green functions and their irreducible proper vertices. We find as well formal equations, governing by the generating functionals of systems which possess a symmetry with respect to a field variation and are subjected to an arbitrary constrain. Finally, we generalize field-theoretical schemes inherent in concrete calculi in the Naudts spirit.Comment: 12 pages, 3 figure

Stripe phase: analytical results for weakly coupled repulsive Hubbard model

Motivated by the stripe developments in cuprates, we review some analytical results of our studies of the charge- and spin density modulations (CDW and SDW) in a weakly coupled one dimensional repulsive electron system on a lattice. It is shown that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wave vectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, not only the wave vectors, but also the mutual phases of the CDW and SDW become coupled due to a quantum interference phenomenon, leading to the stripe phase instability in a quasi one-dimensional repulsive electron system. It is shown that away from half filling periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential causes vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group (parquet) analysis away from half filling are also presented, which indicate transient-scale correlations resembling the mean-field pattern. Farther, the self-consistent solution for the spin-charge solitonic superstructure in a quasi-one-dimensional electron system is obtained in the framework of the Hubbard model as a function of hole doping and temperature. Possible relationship with the stripe phase correlations observed in high T_c cuprates is discussed.Comment: 29 pages,10 figures, Late

Quantization of bosonic fields with two mass and spin states

We investigate bosonic fields possessing two mass and spin states. The density matrix in the first order formalism is obtained. The quantization of fields in the first order formulation is performed and propagators are found.Comment: 9 page

The high probability state transfers and entanglements between different nodes of the homogeneous spin 1/2 chain in inhomogeneous external magnetic field

We consider the high probability state transfers and entanglements between different nodes of the spin-1/2 chains governed by the XXZ-Hamiltonian using the inhomogeneous stationary external magnetic field. Examples of three-, four-, ten- and twenty-node chains are represented. A variant of realization of the proper inhomogeneous magnetic field is discussed.Comment: 16 pages, 2 figure