Relativistic nuclear corrections to the spin structure function of the deuteron in the light-cone variables

The relativistic deuteron has been considered in the light-cone formalism as a system of two strongly interacting nucleons (two-nucleon approximation). The technique for the calculation of the average helicity of the proton in the deuteron has been considered in the light-cone variables. A receipt has been pro-posed for the consistent calculation of relativistic nuclear corrections to the average helicity of the proton in the deuteron and to the spin structure function of the deuteron g ₁ ^D . Relativistic-correction-induced change in the Bjorken sum rule has been discussed.     

Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences Zitterbewegung, represents a gauge non-invariant variable in our model. Hence our particle does not experience the undesirable Zitterbewegung. C) In the non-relativistic limit spin is described by three-vector, as it could be expected.     

Study of relativistic bound state wave functions in quasielastic (e,e′ p) reactions

The unpolarized response functions of the quasielastic ¹⁶O(e,e′ p)¹⁵N reaction are calculated for three different types of relativistic bound-state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density-dependent relativistic Hartree calculations that reproduce the experimental rms charge radius of ¹⁶O. The sensitivity of the unpolarized response functions to the single-particle structure of the different models is investigated in the relativistic plane-wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single-particle states. The interference responses R_LT and R_TT reveal a strong sensitivity to the small component of the relativistic bound-state wave function.     

Statistical mechanics of relativistic plasmas

Based on the Klimontovich method of construction of a relativistic statistical mechanics the binary correlation function of a relativistic plasma is considered. Up to the order e⁴ for spatially homogeneous systems the relativistic binary correlation function can be expressed by the relativistic dielectric tensor, where higher-order correlation functions are neglected.In the case of thermodynamic equilibrium the relativistic dielectric tensor is calculated. The corresponding binary correlation function is determined up to the first relativistic order. The result is compared with those of Trubnikov/Kosachev (1968) and Krizan (1969).     

Relativistic corrections in coupled channel mixing

We examine relativistic effects in a coupled channel mixing calculation of corrections to charmonium energy levels. We find that the relativistic effect on the coupled channel mixing is large. Thus a relativistic treatment is necessary and may possibly lead to a larger admixture ofD andS states.     

Relativistic non-Hamiltonian mechanics

Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u_μu^μ + c² = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton’s principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton’s principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton’s principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton’s principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.     

Influence of relativistic effects on electron-loss cross sections of heavy and superheavy ions colliding with neutral atoms

The influence of relativistic effects, such as relativistic interaction and relativistic wave functions, on the electron-loss cross sections of heavy and superheavy atoms and ions (atomic number Z ? 92) colliding with neutral atoms is investigated using a newly created RICODE-M computer program. It is found that the use of relativistic wave functions changes the electron-loss cross section values by about 20–30% around the cross-section maximum compared to those calculated with nonrelativistic wave functions. At relativistic energies E ≥ 200 MeV/u, the relativistic interaction between colliding particles leads to a quasiconstant behavior of the loss cross sections σ _EL ^rel ～ const, to be compared with the Born asymptotic law σ _EL ^B ～ lnE/E.     

Relativistic study of the reaction pp → dπ: Formalism and comparison with experiment at Tp = 578 MeV

A detailed relativistic calculation of pp → πd is presented. The leading graph is the exchange of a nucleon and a pion. The πN amplitudes, including off-shell information, are input, together with relativistic dpn and πNN vertex functions. The dominant nucleon spectator term is calculated without uncontrolled approximations, and the relativistic pion antiparticle contribution is evaluated. The single nucleon exchange diagram is added. Higher order rescattering is treated by initial and final state distortion factors. All amplitudes and spin observables are calculated and a detailed comparison with the measured data at 578 MeV is made. The remaining observed discrepancies are traced to the pp spin-triplet waves.     

Positronium and Muonium in strong magnetic fields

The relativistic two-body problem in a constant magnetic field B of arbitrary strenght is elaborated. A new spin operator quadratic in B is derived and a change of sign in a relativistic Zeeman correction is pointed out.     

Relativistic and separable classical hamiltonian particle dynamics

We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincaré invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincaré invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light.     

On classical and quantum relativistic dynamics

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added.     

Interacting relativistic boson fields in the De Sitter universe with two space-time dimensions

The positive temperature Gibbs state of a scalar boson field with a relativistic local self-interaction in two space-time dimensional Minkowski universe as constructed in [1] is not relativistic invariant. We prove in this paper that the corresponding state in the De Sitter universe is actually relativistic invariant if the temperature is given byT=1/2πR whereR is the constant radius of curvature of the De Sitter universe. Moreover the construction gives that the Schwinger functions or imaginary time Wightman functions are the moments of a generalized Markoff process on the sphere of radiusR.     

Cutting DNA: Mechanics of the topoisomerase

The framework of relativistic self-consistent mean-field models is extended to include correlations related to restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The model, currently restricted to axially symmetric shapes, employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a δ-interaction in the pairing channel. Both bulk and spectroscopic nuclear properties are explored.     

Functional integrals for order-disorder variables in terms of Bohm-Aharonov strings

We generalize our previously presented framework for the functional integral formalism of kinks and disorder variables to the direct construction of order variables in relativistic two-dimensional spinor theories. The important new objects here are “_γ5 Bohm-Aharonov strings”. We choose as an illustration the construction of the order variable in the Ising field theory. A _γ5 string brings about a C self-conjugate normalizable mode which has a more subtle nature than the _γ5 skew Atiyah-Singer 't Hooft zero modes. As a result there is a transmutation of quantum numbers similar to that observed with the help of the quasiclassical methods of Jackiw, Rebbi, 't Hooft and Hasenfratz.     

Relativistic corrections to quantum mechanical concept ofJ/ψ formation time

The effect ofJ/ψ dissolution in quark-gluon plasma is calculated within quantum mechanical approach taking into account also relativistic corrections. It is found that relativistic effects do not influence significantly the time dependence of theJ/ψ dissolution. Consequently the rate ofJ/ψ suppression is not dramatically changed.     

Effect of temperature on $$\mathbf{In}_{{\varvec{x}}} \mathbf{Ga}_{1-{{\varvec{x}}}} \mathbf{As}/\mathbf{GaAs}$$ quantum dots

Analytical solution of the Dirac equation for the modified Pöschl–Teller potential and trigonometric Scarf II non-central potential for spin symmetry is studied using asymptotic iteration method. One-dimensional Dirac equation consisting of the radial and angular parts can be obtained by the separation of variables. By using asymptotic iteration method, the relativistic energy equation and orbital quantum number (l) equation can be obtained, where both are interrelated. Relativistic energy equation is calculated numerically by the Matlab software. The increase in the radial quantum number n _r causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in terms of hypergeometric functions. Some thermodynamical properties of the system can be determined by reducing the relativistic energy equation to the non-relativistic energy equation. Thermodynamical properties such as vibrational partition function, vibrational specific heat function and vibrational mean energy function are expressed in terms of error function.     

Relativistic Zeeman effect in positronium,n=2

Approximate relativistic center-of-mass variables are employed for the calculation of the relativistic corrections to the Zeeman structure of then=2 energy level of positronium.     

Relativistic quantum particle in a homogeneous external field

The model of the relativistic quantum particle in a homogeneous external field is proposed. This model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space in our case is the one-dimensional Lobachevsky space. We have found the wave functions and propagator for the model under study in both x- and p-representations.     

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example.