Conjugaisons finies et milieux continus en relativité générale

We present here the main elements of a mechanics of relativistic continua relying upon a concept of 《finite conjugacy》 between two relativistic motions described by two unit vector-fields u and u' defined on two different relativistic manifolds $\text{M}$-and $\text{M}$'.This purely relativistic, global, and intrinsic theory leads, together with a new approach of the deformation tensors in relativity, to a differential system of equations for the conjugacies which is neither under-determined nor over-determined. A rough study of the propagation of the conjugacy-waves shows then that it is advisable to consider the notion of a finite conjugacy as a satisfying relativistic extension of the classical and tridimensional notion of a finite deformation in mechanics, and to identify the spatial conjugacy-waves obtained with the ordinary acoustic waves.Drastic particularizations of the space-times $\text{M}$ and $\text{M}$', of the motions u and u', of the admissible types of conjugacies and of the elastic behaviour of the continua under study allow to recover, as very important but particular cases, the tridimensional non-relativistic theory of elasticity for finite deformations and non-linear behaviour, as well as the main theories of relativistic elasticity already proposed by Mmes Choquet-Bruhat and Lamoureux-Brousse, Rayner, Carter and Carter-Quintana, Grot-Eringen…. The obtained system of equations generalizes also to the finite case some aspects of the infinitesimal theory of Weber and Papapetrou.     

Intersections of quasi-energy levels in the relativistic theory of multiply charged ions

The relativistic generalization of the quasi-energy method is given with the help of which the influence of an alternating electric field on the energy levels (2 $\text{1}\text{2}$ 0), (2 $\text{1}\text{2}$ 1) of multiply charged H-like ions is investigated. Intersections are found of quasi-energy levels in external fields with frequencies ω₀ ? ΔE_L and definite values of the field amplitude.     

Relativistic kinetic theory of quantum systems: I. Wigner functions for a relativistic spin-12 system

For a dilute and nondegenerate relativistic spin-$\text{1}\text{2}$ system two kinds of Wigner functions are defined: one has sixteen spinor components and the other four spin components. Their relationship is established. Statistical expressions for the current density, the energy-momentum density and the spin density are obtained in terms of both kinds of Wigner functions. The transformation properties of the latter under Lorentz transformations are discussed.     

Resonance magnetic field shift induced by electric field for the +12→-12 transition relativistic approach

The resonance magnetic field shift induced by an electric field for the $\text{+}\text{1}\text{2}\text{→-}\text{1}\text{2}$ transition has been interpreted using a relativistic spin motion equation. Two examples are reported.     

Orbital classical solutions,non-perturbative phenomena and singularity at the zero coupling constant point

We try to extend previous arguments on orbital classical solutions in non-relativistic quantum mechanics to the $\text{1}\text{4}\text{λ|φ|}{}^4$ complex relativistic field theory. The single valuedness of the Green function in the semiclassical $\text{(}\text{h}\text{?}\text{→ 0)}$ limit leads to a Bohr-Sommerfeld quantization. A path integral formalism for the Green functions analogous to that in non-relativistic quantum mechanics is employed and a semiclassical approach which uses our classical solutions indicates non-perturbative effects. They reflect and $\text{e}{}^{\mathrm{<mtext>1</mtext><mtext>\lambda </mtext>}}$ singularity at the zero coupling constant point.     

Asymptotic freedom,light quarks and the origin of the ΔT = 12 rule in the non-leptonic decays of strange particles

A dynamical mechanism for the $\text{ΔT =}\text{1}\text{2}$ rule in the non-leptonic decays of strange particles is considered. The weak interactions are described within the Weinberg-Salam model while the strong interactions are assumed to be mediated by the exchange of an octet of colour vector gluons. It is shown that the effect of the strong interactions gives rise to new operators in the effective Hamiltonian of weak interactions which contain both left- and right-handed fermions. These operators satisfy the $\text{ΔT =}\text{1}\text{2}$ rule, and estimates within the relativistic quark model indicate that their contribution dominates the physical amplitudes of the K → 2π, 3π decays.     

On the relativistic Thomas-Fermi model

The relativistic generalization of the Thomas-Fermi model of the atom is derived. It approaches the usual nonrelativistic equation in the limit Z ? Z_crit, where Z is the total number of electrons of the atom and $\text{Z}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{α}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ and α is the fine structure constant. The new equation leads to the breakdown of scaling laws and to the appearance of a critical charge, purely as a consequence of relativistic effects. These results are compared and contrasted with those corresponding to N self-gravitating degenerate relativistic fermions, which for $\text{N ≈ N}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(m/m}{}_{\mathrm{<mtext>p</mtext>}}\text{)}{}^3$ give rise to the concept of a critical mass against gravitational collapse. Here m is the mass of the fermion and $\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{=(?c/G)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is the Planck mass.     

Neutrino-excitation of baryon resonances and single pion production

This is an attempt to describe all existing data on neutrino production of single pions in the resonance region up to W = 2 GeV in terms of the relativistic quark model of Feynman, Kislinger and Ravndal (FKR). We considered single pion production to be mediated by all interfering resonances below 2 GeV. A simple noninterfering, nonresonant background of isospin $\text{1}\text{2}$ was added. It improved agreement with experiment, particularly in the ratio of isospin amplitudes in charged current reactions, at the expense of one additional constant. All total cross sections, cross section ratios and W-distributions are well reproduced at low and high energies, with charged and neutral currents (supposing the Salam-Weinberg theory with sin²$\text{θ}{}_{\mathrm{w}}\text{≈}\text{1}\text{4}$ to be correct), and for neutrinos and antineutrinos, giving predictions where data are lacking. New predictions have been made for complex angular distributions in $\text{N}$π channels exhibiting strong interference between neighbouring resonances. These are sensitive (for 1.1 GeV ? W ? 1.5 GeV) to the sign of the Roper resonance P₁₁(1450) which is controversial in photoproduction experiments.     

Relativistic corrections to the Zeeman effect in diatomic molecules

Basic molecular g-factors for the ²Π ground states of OH, SH, NO, NS, and ClO have been determined by a weighted nonlinear least squares fit including zero-field as well as Zeeman data. The combined g-factor $\text{g}{}_{\mathrm{l}}\text{+}\text{1}\text{2}\text{g}{}_{\mathrm{s}}$ accounts for the dominant contribution to the Zeeman effect of the paramagnetic ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ substate. Theoretical values of $\text{g}{}_{\mathrm{l}}\text{+}\text{1}\text{2}\text{g}{}_{\mathrm{s}}$ have been computed by considering the relativistic corrections arising from the reduction of the Breit equation to the second Pauli limit, and a contribution due to the motion of the nuclear center of mass is also included. The relativistic corrections have been computed by use of known LCAO molecular wavefunctions. Furthermore the free electron quantum electrodynamic correction ($\text{α}\text{2}\text{Π}$) to g_s is used as an ad hoc value for an electron bound to a diatomic molecule. A systematic difference is found between theoretical and fitted values of $\text{g}{}_{\mathrm{l}}\text{+}\text{1}\text{2}\text{g}{}_{\mathrm{s}}$. The difference increases linearly with the parameter $\text{Y = |}\text{A}\text{B}\text{|}$ for the molecules OH, SH, and NO. The maximum difference is encountered for NO and is about 20% of the free electron quantum electrodynamic correction. With further increase in Y (NS and ClO) the agreement seems to improve again.     

On duality in e+e- annihilation

With the help of a relativistic generalization of a formula for the leptonic width of quarkonium in the quasiclassical approximation it is shown that the sum of a sufficiently large number of total cross sections for the production of the quarkonium state (Q$\text{Q}$)_n in e⁺e^- annihilation is equal to the total cross section for production of a quasi-free quark- antiquark pair Q$\text{Q}$.     

On a possible test of massive high spin wave equations in heavy-ion scattering

Cross sections and polarization functions for elastic scattering of identical particles with spin 1 are compared in the relativistic $\text{(s,0)+(s?}\text{1}\text{2}\text{,}\text{1}\text{2}\text{)}$ invariant theory, for arbitrary spin, and the $\text{(}\text{1}\text{2}\text{,}\text{1}\text{2}\text{)}$ invariant Proca theory. Heavy-ion scattering is suggested to test high spin theories.     

Dynamical group quantization

The projective unitary irreducible representations U(G) of the space-time symmetry group G provides a unique quantization scheme for elementary particles. By extension a direct method of quantization for more general systems by the projective unitary representations U^$\text{G}$(G) induced from a dynamical group $\text{G}$ is outlined. Reducible relativistic composite systems are defined and the geometry of $\text{G}$ is discussed.     

Quantum theory of a free electron in a tapered wiggler field

It is pointed out that a slight modification of the relativistic quantum theory of a free electron in a uniform wiggler field enables the study of motion in a tapered wiggler field of the form $\text{k}{}_{\mathrm{w}}{}^1\text{= k}{}_{\mathrm{w}}\text{?}\text{b}\text{z}$ which merits attention. The lower limit of z is 800 cm. The exact relativistic quantum mechanical calculation shows an enhancement in the gain for single pass. The frequencies are up-shifted by amounts depending on the parameter b.     

High accuracy energy-level calculations of the rotational-vibrational weakly bound states of ddμ and dtμ mesic molecules

Calculations are performed of the nonrelativistic energies $\text{E}{}_{\mathrm{JV}}$ of rotational-vibrational weakly bound states J = ν = 1 of ddμ and dtμ mesic molecules: $\text{E}{}_{11}\text{(}\text{dd}\text{μ) = ? 1.956}\text{eV}$ and $\text{E}{}_{11}\text{(}\text{dt}\text{μ) = ? 0.656}\text{eV}$ with an accuracy of 0.001 eV. With the relativistic effects and nuclear finite size corrections taken into account the result is: $\text{E}{}_{11}\text{(}\text{dd}\text{μ) = ? 1.946}\text{eV}$ and $\text{E}{}_{11}\text{(}\text{dt}\text{μ) = ? 0.634}\text{eV}$.     

Relativistic effect on magnetic moments of negative muons bound to high-Z nuclei

The g factors of the negative muons bound to Zn, Cd, and Pb nuclei have been determined. The observed values after the corrections for the internal fields have shown substantial deviations from the free-muon g factor: $\text{(g}{}_{\mathrm{<mtext>free</mtext>}}\text{-g)}\text{g}{}_{\mathrm{<mtext>free</mtext>}}$ is (1.3±0.6)% for Zn, (2.2±1.4) % for Cd, and (5.0±2.2)% for Pb. These shifts are in good agreement with the relativistic binding corrections for finite-size nuclei calculated by Ford et al.     

Magnetic flux lines as relativistic strings

It is suggested that the relativistic string of the dual resonance model of hadrons is a line of quantised magnetic flux. Accordingly, quarks have magnetic charge. Assuming quarks of magnetic charge ${}^{\mathrm{+}}\text{g,?g}$, baryons are composed of three quarks. States of one, two, four or five quarks will not normally occur.