Boson-fermion symmetries and superfields

This review provides an introduction to the theory of supersymmetry. The algebra of supersymmetries is developed, and its representations are given together with the ensuing surprising property of vanishing of the vacuum average of the energy-momentum tensor in supersymmetrical theories. Particular attention is paid to superfields–objects that combine fermion and boson fields with the aid of auxiliary anticommuting spinor coordinates. The Lagrangian formalism and the equations of motion for superfields are discussed. A detailed analysis is presented of the simplest supersymmetrical model of a chiral scalar superfield and its exceptional renormalizability. Gauge supersymmetrical theories are analyzed. The possibilities are discussed of a nontrivial unification of internal symmetries and supersymmetries. The article concludes with first attempts of spontaneous supersymmetry breaking, which is needed for the construction of future realistic supersymmetrical models.