Non-relativistic Reduction of Spinors, New Currents and their Algebra
arXiv:1907.06343 · doi:10.1016/j.nuclphysb.2020.114994
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
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- Gauge interactions and the Galilean limit