Residual symmetries in the presence of an EM background

The symmetry algebra of a QFT in the presence of an external EM background (named "residual symmetry") is investigated within a Lie-algebraic, model-independent scheme. Some results previously encountered in the literature axe extended here. In particular we compute the symmetry algebra for a constant EM background in D = 3 and D = 4 dimensions. In D = 3 dimensions the residual symmetry algebra, for generic values of the constant EM background, is isomorphic to u(1) circle plus P-c(2), with P-c(2) the centrally extended two-dimensional Poincare algebra. In D = 4 dimension the generic residual symmetry algebra is given by a seven-dimensional solvable Lie algebra which is explicitly computed. Residual symmetry algebras are also computed for specific non-constant EM backgrounds and in the supersymmetric case for a constant EM background. The supersymmetry generators are given by the "square roots" of the deformed translations.