Canuto 1971

Canuto, V., 1971: Quantum-mechanical relation for a magnetized electron gas. Phys. Rev. A, 3, 648-650, doi:10.1103/PhysRevA.3.648.

The following theorem is proven: The xx and zz components of the electron energy-momentum tensor t_μν and the magnetization M of an electron gas in a constant magnetic field B satisfy the relation t_zz-t_xx = BM. This relation is valid at any density, temperature, and magnetic field strength, if the system is in thermal equilibrium. Since the electromagnetic energy-momentum tensor t_μν is anisotropic itself, this relation makes the total energy-momentum tensor T_μν = t_μν + τ_μν become a scalar. Because t_xx and t_zz can simply describe the electron pressure in these directions, the above theorem states that the difference p_zz-p_xx equals twice the magnetic field energy, since M = 4πB.

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Canuto, V.: Quantum-mechanical relation for a magnetized electron gas, Phys. Rev. A, 3, 648-650, doi:10.1103/PhysRevA.3.648, 1971.

Canuto, V. (1971), Quantum-mechanical relation for a magnetized electron gas, Phys. Rev. A, 3, 648-650, doi:10.1103/PhysRevA.3.648.

Canuto, V., 1971: Quantum-mechanical relation for a magnetized electron gas. Phys. Rev. A, 3, 648-650, doi:10.1103/PhysRevA.3.648.

Canuto, V. 1971, Phys. Rev. A, 3, 648, doi:10.1103/PhysRevA.3.648.

Canuto V. Quantum-mechanical relation for a magnetized electron gas, Phys Rev A 1971;3:648-650. doi:10.1103/PhysRevA.3.648.

V. Canuto, Phys. Rev. A 3, 648-650, doi:10.1103/PhysRevA.3.648 (1971).