Many-particle Correlation Effects and Magnetism of Weakly Relativistic Electron Gas

The path integral quantum-statistical approach to study the magnetic properties of the weakly relativistic interacting electron gas in the inhomogeneous magnetic eld is suggested. In the random phase approximation the thermodynamic potential is calculated. In the case of absolute zero the magnetization and nonlinear magnetic susceptibility of the system are found. Both Landau diamagnetism and Pauli paramagnetism are taken into account. It is shown that in the region of high electron density the relativistic contributions are essential and lead to the increase of magnetic susceptibility. Classical and quantum treatment of the magnetic properties of relativis-tic ideal electron gas was given in ref. 1,2]. The many-particle corrections (including correlation contributions) to the magnetic susceptibility of the non-relativistic electron gas are discussed in ref. 3]. For the relativistic description of the interacting charged spin particles the spin-spin, spin-orbital, contact, Coulomb and retarded electromagnetic interactions, as well as the interaction with external eld are necessary to take into account. Explicit form of the relativistic interactions is complicated and consequently the construction of the corresponding statistical theory is complicated, as well. However for the weakly relativistic case there is a possibility of statistical description analogous to the non-relativistic theory 4]. In the present paper an approach to the quantum-statistical theory of the magnetism of the interacting weakly relativistic electron gas is suggested. Such approach is based on the Lagrange description and path integral formalism. This formalism was developed in papers 4,5]. The Lagrangian of the weakly relativistic electron gas in the presence of the external inhomogeneous magnetic eld H 0 (r) = rotA 0 (r) is as follows