  The physical and mathematical mechanism behind diamagnetism of N (finite)
spinless bosons (relativistic or non-relativistic) is well known. The
mathematical signature of this diamagnetism follows from Kato's inequality
while its physical way of understanding goes back to Van Leewen. One can guess
that it might be true in the field theoretic case also. While the work on
systems with a finite number of degrees of freedom suggests that the same
result is true in a field theory, it does not by any means prove it. In the
field theoretic context one has to develop 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 charged spinless bosons to the case of infinite degrees of freedom. We also
discuss possible applications of the theory.
