Quantum Theory of an Electron Gas in Intense Magnetic Fields

Abstract

In this paper we have developed the quantum theory of a relativistic electron gas in magnetic fields of arbitrary strength, and we have obtained the equation of state for such a gas. Intense magnetic fields (of field strengths ^10 13 G) are believed to exist during gravitational collapse and in collapsed astronomical objects. Our results show that the stress tensor is very anisotropic when (p z 2 )/m 2 c 2 \_p z -(z momentum) = (momentum parallel to the field)] is smaller than (2H/H^) l t % t where H is the field and E c -m 2 c % l'he-^A\^ X10 13 G. At a temperature of 10 9 °K or a density of 10 6 g/cm 3 , the theory developed here must be used if #>10 12 G.

Magnetism in Dense Quark Matter

“…[66], but using a functional-method approach that makes it easier to recognize the thermodynamical quantities entering in the final results. An advantage of the procedure followed in [66], as compared with that of [27], is that it does not assume that the fermion fields entering in the definitions of the energy and pressures satisfy the classical equation of motions (i.e. the Dirac equations for ψ and ψ), but the functional integrals integrate in all field configurations.…”

“…Hence, the terms depending on the Lagrangian density L ψ in τ µν were kept, while in Ref. [27] the condition L ψ = 0 was considered as a constraint.…”

“…These calculations were carried out long time ago in Ref. [27], using a QFT second-quantization approach. There, a quantum-mechanical average of the energymomentum tensor in the eigen-states of the Dirac equation in the presence of the uniform magnetic field was first performed to get the corresponding quantum operator in the occupation-number space.…”

Field-induced degeneracy regimes in quantum plasmas

“…(18) and (19). The third condition, however, can be directly evaluated using the pseudopotentials for both quantized degeneracy.…”

“…The earliest extensive study of this kind belongs to Canuto and Chiu [15][16][17][18][19][20][21][22]. It has been shown [17,23] that the electronic density of state, hence all thermodynamics quantities, become quantized due to the familiar Landau orbital quantization.…”