Quantum Theory of an Electron Gas in Intense Magnetic Fields

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 ∼10¹³ 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_z²〉 / m²c² [p_z=(z momentum)=(momentum parallel to the field )] is smaller than (2H / H_c)^{1 / 2}, where H is the field and H_c=m²c³ / ℏe=4.414×10¹³ G. At a temperature of 10⁹ °K or a density of 10⁵ g/cm³, the theory developed here must be used if H≳10¹² G.