Modified Gibbs's representation of rotation matrix

A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and Cayley$-$Klein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained. The composition law of two rotations from the quaternion representation is presented showing a convenient expression for calculating the successive rotations.Comment: 17 page

A dense Bose fluid at zero temperature: condensation and clusters in liquid He-4

We present a full set of wave equations describing a dense Bose fluid, applicable both to non- ideal gases and to liquid 4He. The phonon spectrum in liquid 4He is found and the fraction of condensed particles is calculated at zero temperature for a wide range of densities. The theory also yields the ground-state energy for the quantum liquid 4He in agreement to high accuracy with Monte Carlo simulations and experimental data at low pressure. We also present the derivation of a generalized Hartree-Fock equation describing roton clusters in low temperature liquid 4He, allowing us to confirm that, at low enough temperatures and for a wide range of pressures, the stable clusters consist of 13 bound atoms.Comment: 16 pages, 7 figure

Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance

Kalb-Ramond equations for massive and massless particles are considered in the framework of the Petiau-Duffin-Kemmer formalism. We obtain $10\times10$ matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy-momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.Comment: 9 pages, no figure

Effective Lagrangian and Dynamical Symmetry Breaking in the SU(2)XU(1) NJL Model

Dynamical symmetry breaking and the formation of scalar condensates in the SU(2)XU(1) Nambu-Jona-Lasinio model with two coupling constants has been studied in the framework of the mean field approximation. The bosonization procedures of the model are performed using the functional integration method. The possibility of the spontaneous CP symmetry breaking in the model under consideration has been shown. The mass spectrum of the bound states of fermions, as well as the effective Lagrangian of interacting scalar and pseudoscalar mesons are obtained.Comment: 7 pages, LaTeX. Minor correction

Solutions of Podolsky's Electrodynamics Equation in the First-Order Formalism

The Podolsky generalized electrodynamics with higher derivatives is formulated in the first-order formalism. The first-order relativistic wave equation in the 20-dimensional matrix form is derived. We prove that the matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The Hermitianizing matrix and Lagrangian in the first-order formalism are given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin projections are obtained, and we find the density matrix for the massive state. The $13\times 13$-matrix Schrodinger form of the equation is derived, and the Hamiltonian is obtained. Projection operators extracting the physical eigenvalues of the Hamiltonian are found.Comment: 17 pages, minor corrections, published versio

Effects of x(3) nonlinearities in traveling-wave second-harmonic generation

We investigate the effects of self-phase and cross-phase chi ((3)) nonlinearities, in the process of traveling-wave second-harmonic generation. We derive a semiclassical analytical solution for the field intensities, comparing this with the numerically obtained fully quantum solutions. We also investigate the effects of the cross-phase modulation on the quantum statistical properties of the fields. We find that, as the chi ((3)) components increase, there are qualitative changes to both the field intensities and the quantum statistics

Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity

Using the numerical solution of the nonlinear Schr\"odinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.Comment: 4 pages, 3 PS figure

On Hyperbolic Attractors in Complex Shimizu -- Morioka Model

We present a modified complex-valued Shimizu -- Morioka system with uniformly hyperbolic attractor. The numerically observed attractor in Poincar\'{e} cross-section is topologically close to Smale -- Williams solenoid. The arguments of the complex variables undergo Bernoulli-type map, essential for Smale -- Williams attractor, due to the geometrical arrangement of the phase space and an additional perturbation term. The transformation of the phase space near the saddle equilibrium "scatters" trajectories to new angles, then trajectories run from the saddle and return to it for the next "scatter". We provide the results of numerical simulations of the model and demonstrate typical features of the appearing hyperbolic attractor of Smale -- Williams type. Importantly, we show in numerical tests the transversality of tangent subspaces -- a pivotal property of uniformly hyperbolic attractor.Comment: 9 pages, 8 figure