BOSE-EINSTEIN CONDENSATION OF A CHARGED RELATIVISTIC IDEAL-GAS IN A GENERAL HOMOGENEOUS MAGNETIC-FIELD

It is shown how the effective action formalism and zeta-function regul arization can be used to study Bose-Einstein condensation for a relati vistic charged scaler field in a general homogeneous magnetic field in a spacetime of arbitrary dimension. In the special case where the mag netic field has only one component, Bose-Einstein condensation occurs at high temperature only for D greater than or equal to 5 where D is t he spatial dimension. When Bose-Einstein condensation does occur the g round-state expectation value of the scalar field is not constant and we determine its value. If the magnetic field has p independent nonzer o components we show that the condition for Bose-Einstein condensation is D greater than or equal to 3 + 2p. In particular, Bose-Einstein co ndensation can never occur if the magnetic field has all of its indepe ndent components nonzero. The problem of Bose-Einstein condensation in a cylindrical box in D spatial dimensions with a uniform magnetic fie ld directed along the axis of the cylinder is also discussed.