M. P. B\'eccar Varela, M. C. Caputo, M. B. Ferraro, P. Lazzeretti,M. C. Mariani,D. Rial
Some mathematical properties of 
gauge transformations with respect to the Coulomb's gauge: variational analysis 
of an energy functional
(55K, Latex)

ABSTRACT.  As gauge invariance of computed magnetic properties, usually partitioned into 
diamagnetic and paramagnetic terms, is not achieved within the 
algebraic approximation, unless {\sl ad hoc} techniques are adopted, 
a general variational treatment is analyzed, attempting to minimize the term 
more difficult to evaluate accurately, i.e., the 
paramagnetic contribution to magnetic susceptibility, by means of a gauge 
transformation. It is shown that an absolute minimum in a 
variational sense cannot be determined a priori. However, a `local' minimum 
of the paramagnetic contribution to 
magnetic susceptibility can be arrived at by 
employing general gauge transformations 
of polynomial form.