Non-relativistic Reduction of Spinors, New Currents and their Algebra

Abstract

A specific mapping is introduced to reduce the Dirac action to the non-relativistic (Pauli - Schrödinger) action for spinors. Using this mapping, the structures of the vector and axial vector currents in the non-relativistic theory are obtained. The implications of the relativistic Ward identities in the non-relativistic limit are discussed. A new non-abelian type of current in the Pauli - Schrödinger theory is obtained. As we show, this is essential for the closure of the algebra among the usual currents. The role of parity in the non-relativistic theory is also discussed.

19 pages, No figures V2 shortened, main results unchanged, version to appear in Nuclear Physics B