abstract

The Mathisson–Papapetrou equations are used to study the deviation of the spinning particle world lines and trajectories from the corresponding geodesic lines in Schwarzschild’s background. The traditional form of these equations and their consequences in terms of the comoving tetrads are considered. Analytical and numerical calculations for the equatorial motions are performed. The circular, quasi-circular, and quasi-radial motions of the highly relativistic spinning particle are analyzed. Different illustrations are presented.

abstract

We show that the rank decomposition of a real matrix \(r\), which is a Spin(3,1) tensor, leads to \(2k\) Majorana bispinors, where \(k= \mathrm {rank}\: r\). The Majorana bispinors are determined up to local GL\((k, \mathbb {R})\) transformations. The bispinors are combined in pairs to form \(k\) complex Dirac fields. We analyze in detail the case \(k=1\), in which there is just one Dirac field with the well-known standard Lagrangian. The GL\((1, \mathbb {R})\) symmetry gives rise to a new conserved current, different from the well-known U(1) current. The U(1) symmetry is present too. All global continuous internal symmetries in the \(k=1\) case form the SO(2,1) group. As a side result, we clarify the discussed in literature issue whether there exist algebraic constraints for the matrix \(r\) which would be equivalent to the condition \(\mathrm {rank}\: r=1\).

abstract

Using an expanded Brueckner–Hartree–Fock (BHF) framework with a phenomenological three-body force (3BF), we study the microscopic characteristics and equation of state (EOS) of symmetric nuclear and neutron matter. Both symmetric nuclear and pure neutron matter are used in the \(G\)-matrix computations, which are carried out by adding the 3BF to the initial two-body force (2BF) and employing a partial wave expansion. Using an angle-average and accurate Pauli operator, the single-particle potential is applied in both its standard and continuous forms. The fourth-order charge-dependent chiral nucleon–nucleon contact of the N3LO potential was used for the computations, both with and without the three-nucleon Urbana interaction included. It was found that the BHF approximation significantly improves the computations for symmetric nuclear matter at high density when one uses only the N3LO potential. As a matter of fact, it is shown that the 3BF is required for reproducing the empirical saturation property of symmetric nuclear matter in a non-relativistic microscopic framework and significantly alters the EOS of nuclear matter at huge densities above the typical nuclear matter density. A crucial component of the estimated equation of state of isospin-asymmetric nuclear matter is the nuclear symmetry energy. It establishes the structure of neutron stars and finite nuclei.

abstract

With the increasingly serious population aging, people pay more attention to the operation and management of pension. The optimization of pension investment has attracted the research interest of many scholars. Firstly, an asset price model is established by using the non-extensive statistical theory, which can well describe the high-peak and fat-tail characteristics of asset returns. Then, under the mean-variance criterion, the optimal investment model of a defined-contribution pension is constructed. Moreover, the explicit solution to the optimal investment strategy of defined-contribution pension is obtained by using dynamic programming, Legendre transformation, and duality theory. This conclusion not only broadens the application of non-extensive statistics in the financial field, but also provides a new theory for the investment of pension funds.