Current algebra and Wess-Zumino terms: a unified geometric treatment

Abstract

The effect of the occurrence of a semi-invariant Wess-Zumino term in a Lagrangian theory upon the realization of a symmetry in terms of the algebra of currents is analysed. The general geometrical origin of the modification of the algebra is exhibited for two very different theories: the Newtonian particle, whose Lagrangian is shown to be a WZ term, and the G × G chiral field theories in even dimensions when their action includes a WZ piece. For the latter our analysis provides an economical approach to the calculation of the so called Schwinger terms which allows us to give their explicit form for any even dimension D and which for D = 2, 4 reduces to the already known expressions.