abstract

We discuss in detail the general-relativistically covariant Dirac equation derived by Fock for a particle of rest mass \(m\) and charge \(e\) in an potential \(A_i\), \([i\gamma ^{\,k}(\partial _k -{\mit \Gamma }_k -i e A_k)-m]\psi =0\). The spinorial affine connection is given in terms of the spin connection \(\omega _{abi}\) and spin operator \(\bar {s}_{ab}\) by the formula \({\mit \Gamma }_i=-\omega _{abi}\bar {s}^{\,ab}\)/4, which follows from the assumption that the curved-space gamma matrices \(\gamma _i\) are covariantly constant, and which we prove to be equivalent to the ‘tetrad postulate’ of van Nieuwenhuizen, that the tetrad \(t_i^{\;\;a}\) is covariantly constant. The intermediate result that \(\gamma _k{\mit \Gamma }_i^{\dagger }\gamma ^{\,k}=0\) is also proven. Extension to dimensionality \(D\) is straightforward, and results in the formula \(\widehat {\mit \Gamma }_{I}=-\hat {\omega }_{abI}\widehat {\bar {s}}^{\,ab}\)/4 for the spinorial connection. Reduction of the five-dimensional Dirac equation to four dimensions has been shown by Klein, in the approximation linear in \(A_i\), to yield in addition an anomalous Pauli mass term \(\frac {1}{2} i\sqrt {\pi G_{\rm N}}\,F_{ij}\ s^{ij}\), which produces a correction to the intrinsic magnetic moment of the electron by the factor \((1+\delta )\), where \(\delta =-\sqrt {1\,/\,\alpha }\,m\,/\,M_{\rm P}=-4.90\times 10^{-22}\), of theoretical interest but beyond the range of current experiment. We also discuss the TCP theorem in curved space-time, with particular reference to the heterotic superstring theory of Gross et al., in the expanding Friedmann Universe. Previously, we have established the interrelationship between non-invariance of the metric under T, defined with regard to comoving time by \(t\,\rightarrow \, -t\), due to general relativity, and non-invariance of the superstring under P, due to the asymmetric construction of the world sheet, which contains only right-moving Majorana fermions, while TP is conserved. This motivates study of C and the dimensional fermionic existence conditions found by van Nieuwenhuizen, Chapline and Slansky, Wetterich and Gliozzi et al.

abstract

Discussed is a model of the two-dimensional affinely-rigid body with the double dynamical isotropy. We investigate the systems with potential energies for which the variables can be separated. The special stress is laid on the model of the harmonic oscillator potential and certain anharmonic alternatives. Some explicit solutions are found on the classical, quasiclassical (Bohr–Sommerfeld) and quantum levels.

abstract

We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force \(\vec {F}\). Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D77, 105008 (2008), we recall that the considered noncommutativity generates additional force terms, which appear in the corresponding Newton equation. We demonstrate that the same force terms can be generated by the proper noninertial transformation of classical nonrelativistic space-time.

abstract

Ten Abelian twist deformations of acceleration-enlarged Newton–Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrated that their contraction limit \(\tau \, \to \, \infty \) leads to the new twisted acceleration-enlarged Galilei spaces.

abstract

The concept of clans, emerging in the context of the negative binomial distribution, is generalized. The generalized clans are themselves produced according to negative binomial distribution. This opens new possibilities for interpretation of mechanisms of particle production processes.

abstract

In the present work, we assume \(D_{s0}(2317)\) meson as the \(c\overline {s}\) state and study its parameters at finite temperature using QCD sum rules. It is calculated the annihilation and scattering parts of spectral function in the lowest order of perturbation theory. Taking into account perturbative two-loop order \(\alpha _{\rm s}\) corrections and nonperturbative corrections up to the dimension six condensates it is investigated the temperature dependences of mass and leptonic decay constant of \(D_{s0}(2317)\) meson.

abstract

The multiplicity, average transverse momentum, and charged particle transverse momentum distributions have recently been measured in LHC experiments. The multiplicity and average transverse momentum grow with beam energy. Such growth is expected in the theory of the Color Glass Condensate, a theory that incorporates the physics of saturation into the evolution of the gluon distribution. We show that the energy dependence of the \(p\overline {p}\) data and the LHC data for \(pp\) scattering at \(\sqrt {s}\geq 200\) GeV may be simply described using a minimal amount of model input. Such a description uses parameters consistent with the Color Glass Condensate descriptions of HERA and RHIC experimental data.

abstract

The role of non-axial shapes in the saddle-point energy of heaviest nuclei is studied in a multidimensional deformation space. The main attention is given to the effect of the high-multipolarity, \(\lambda =6\), non-axial deformations, which is studied for the first time. The analysis is performed within a macroscopic–microscopic approach. Generally, a 10-dimensional deformation space is used in the analysis, but some tests are done in even 13 dimensions. A large number of about 300 even–even heavy and superheavy nuclei with proton number \(98 \leq Z \leq 126\) and neutron number \(134 \leq N \leq 192\) is considered. It is found that the inclusion of the non-axial shapes of the multipolarity \(\lambda =6\) lowers the saddle-point energy relatively little, by up to about 0.4 MeV. Together with earlier results on the effect of the quadrupole (\(\lambda =2\)) and hexadecapole (\(\lambda =4\)) shapes, this indicates for the convergence of the effect to zero, with increasing \(\lambda \). As the ground-state shapes of the considered nuclei are axially symmetric, the discussion also concerns the height of the fission barrier. The heights of our barriers are compared with experimental ones and also with those of other authors.

abstract

When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the arbitrary parameter of scale, which characterizes the size of effective particles in terms of the allowed range of virtual energy changes caused by interactions. This article describes a generic example of the non-locality that characterizes light-front interaction Hamiltonian densities of first-order in an effective coupling constant. The same non-locality is also related to a relative motion wave function for a bound state of two particles.

abstract

A new mechanism is proposed to explain the auxeticity (negative Poisson’s ratio) of foams containing stiff grains. The mechanism involves a stochastic migration of stiff grains into cells with soft edges. When a uniaxial compressive stress is applied the migration gives rise to segregation of vacancies toward the lateral surfaces and, as a consequence, to an effective thinning of the sample, as it should be in auxetics. A 2D model based on the cellular automata concept is used to simulate the phenomenon.

abstract

We propose to search for new wave phenomena in the brain by using interference effects in analogy to the well-known double slit (Young) experiment. This method is able to extend the range of oscillation frequencies to much higher values than currently accessible. It is argued that such experiments may test the hypothesis of the wave nature of information coding.