The set of Jacobi curvature operators (i.e. coefficient matrices from the equation of geodesic deviation) is included in an algebra 2 of fundamental geometrical quantities. An equivalence relation on 2 is defined by the action of local pseudoorthogonal transformation group. For spaces of general relativity the algebraic structure, invariants and the normal forms of Jacobi operators are studied. General properties, examples and the interpretation of bifurcation diagrams characterizing gravitation field distribution are considered.
It is shown that flow-lines form time-like shear-free normal congruence of geodesics only in conformally flat gravitational fields of a perfect and viscous fluid. This is found to be a necessary and sufficient condition that the gravitational fields of a perfect and viscous fluid are conformal to a flat space-time.
The predictions of the integer charged quark model with strictly conserved color quantum numbers for deep inelastic Compton scattering are compared with those of the fractionally charged quark model for the different \(\gamma \) energies. The gluon distribution structure function is derived in the framework of the integer charged quark model.
We consider the motion of a wave packet in the external SU(2) gauge field using the Foldy–Wouthuysen representation for the Dirac equation. We find that a satisfactory description of the motion of the wave packet in terms of a trajectory of a classical particle is possible only when the velocity of the wave packet is sufficiently large. We show that in addition to the vectors of classical spin \(\vec {S}\) and color spin \(\vec {I}\) of the particle, it is necessary to introduce a tensorial dynamical variable [\(J^{ab}\)] describing a mixing of the spin and color spin. On the whole, it turns out that the classical particle has six independent internal dynamical variables, compactly described as an SO(3,1) matrix, due to constraint relations between \(\vec {I}\), \(\vec {S}\) and [\(J^{ab}\)].
Generalization of Jordan–Wigner transformation to three space dimensions is proposed. According to the new prescription the system of free fermions is mapped into a set of locally interacting spins with constraints. The whole procedure is performed in the Hamiltonian formulation of the theory.
A scheme to calculate the hadron multiplicity distributions in \(e^+e^-\)-annihilation, taking into account the quark–gluon cascade on the basis of perturbative QCD and the hadronization stage described by a supernarrow binomial distribution, is proposed.
