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 〈pz²〉m²c² [pz=(z momentum)=(momentumparalleltothefield)] is smaller than (2HHc)1/2, where H is the field and Hc=m²c³e=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 H10¹² G.