Diagram and superfield techniques in the classical superalgebras

Abstract

Introduces the concept of 'graded permutation group' in the analysis of tensor operators in the classical superalgebras. For U(m/n) and SU(m/n), irreducible tensor representations correspond to classes of Young tableaux with definite graded symmetry type. Diagram techniques are given for Kronecker products, dimensions, and branching rules. The tensor techniques are complemented by the introduction of a superfluid formalism, in which U(m/n) and SU(m/n) act on (polynomial) functions over the appropriate superspace. Such superfluids may admit constraints. A general superfield interpolates between the classes of Young tableaux which correspond to particular types of constraint. The tensor and superfield techniques are illustrated with case studies of SU(2/1) and SU(m/1).