CHARGED SCALAR FIELDS IN AN EXTERNAL MAGNETIC-FIELD - RENORMALIZATIONAND UNIVERSAL DIAMAGNETISM

The physical and mathematical mechanism behind diamagnetism of N (fini te) spinless bosons (relativistic or non-relativistic) is well known. The mathematical signature of this diamagnetism follows from Kato's in equality while its physical way of understanding goes back to Van Leeu wen. One can guess that it might be true in the field theoretic case a lso. While the work on systems with a finite number of degrees of free dom suggests that the same result is true in a field theory, it does n ot by any means prove it. In the field theoretic context one has to de velop a suitable regularisation scheme to renormalise the free energy. We show that charged scalar fields in (2+1) and (3+1) dimensions are always diamagnetic, even in the presence of interactions and at finite temperatures. This generalises earlier work on the diamagnetism of ch arged spinless bosons to the case of infinite degrees of freedom. We a lso discuss possible applications of the theory.