A theorem known for one-dimensional \(q\)-equivalent Hamiltonians is extended to the multidimensional case. The construction of new integrals of motion is put forward illustrated by the quantity \(\sum _{i,j}\frac {\partial \bar p_i}{\partial p_j}\).
It is shown that Sciama’s inertial force law can be used to provide an explanation of why clusters of galaxies appear to be bound together more than gravitational force from their luminous masses would suggest. Such an explanation gives an approximate value of the constant in the inertial force law. Shortcomings when the law is applied cosmologically are noted. The law is shown not to be amenable to solar system tests, and not to be equivalent to Milgrom’s force law.
In the paper we consider the simple spatially homogeneous and isotropic cosmological models with torsion in the framework of the gauge gravitational theory with quadratic Lagrangian \(L_{\rm g}=\frac {c^4}{16\pi G}({\mit \Omega }^i_{.k}{\mit \Lambda }\eta ^k_i+{\mit \Theta }^i{\mit \Lambda } \ast {\mit \Theta }_i)+\frac {\hslash c}{16\pi }+{\mit \Omega }^i_{.k}{\mit \Lambda }\ast {\mit \Omega }^k_{.i}\). These models were obtained by using of the ansatz \(\frac {\dot a}{ac}+h=(\pm )\frac {1}{a}\).
It is shown that the spectrum generating algebra for the pairing interaction of quarks is the su(4) \(\simeq \) so(6) Lie algebra independently of the \(j\)-shell.
The aim of this paper is purely technical. We want to show the positive points and shortcomings in practical application of the two procedures in quantum field theory. The first — the canonical quantization approach which uses the normal product (NP) and the second procedure, the Feynman path integral approach without the normal product (WNP). To compare both procedures we have made detailed renormalization of the \(\phi ^4\) theory and of the scalar electrodynamics.
The purpose of this paper is to present possible experimental test for the yet unobservable proton structure function \(G_2\). We discuss the Drell–Yan process on transverse polarized proton and antiproton and find the way to measure this function.
Classical Yang–Mills equations for \(x_3\)-dependent, static potentials are investigated. Four classes of solutions are found. All solutions are unstable in the Liapunov sense. The solutions do not exhibit chaotic behaviour in the \(x_3\) variable.
A simple formula for the velocity distribution of nuclei after sequential nucleon evaporation from a compound nucleus is derived. The Gaussian distribution for a single act of nucleon emission was assumed. Results are compared with experimental data.
A barrier penetration model of heavy-ions fusion is presented. To calculate the transmission coefficients through any one-dimensional barrier of nucleus–nucleus real potential a matrix method is used. The parameters of the model are the critical radius and the parameters of nuclear interaction. The model is tested on several cases of fusion, i.e. \(\alpha \) + \(^{40,44}\)Ca, \(^{12}\)C + \(^{12}\)C, \(^{16}\)O + \(^{16}\)O and \(^{12}\)C + \(^{24}\)Mg and it is found to reproduce the data quite well.
Differential cross sections at 0\(^{\circ }\) and 90\(^{\circ }\) measured for \(^{28}\)Si(\(\rho , \gamma _1)^{29}\)P reaction at proton energy range 2.3–2.9 MeV have been analyzed in terms of the direct-semidirect capture model extended by the effective potential approach. Spectroscopic factor of the first excited state of \(^{29}\)P nucleus was found to be 0.10\(\pm \)0.05.
